Math just got important! Which sector of pizza is a better deal! Reddit r/sciencememes
ฝัง
- เผยแพร่เมื่อ 9 ก.ค. 2024
- We have two slices of pizza. One is with a radius of 6 inches and a central angle of 60 degrees while the other is with 7 inches and a central angle of 45 degrees. The first slice costs $1.50 and the second one costs $1.70. Although the prices aren't realistic (unless you are in New York because there are $1 slices), which slice is a better deal?
Original post on Reddit: 👉 / tmmczrfjt2
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1 divided by 0 (a 3rd grade teacher & principal both got it wrong), Reddit r/NoStupidQuestions
th-cam.com/video/WI_qPBQhJSM/w-d-xo.html
"NoStupidQuestions"
How dare you not factor in the crust.
If the radius of pizza is z, and the thickness is a, the volume of the entire pizza is just pizza.
Yes I knew about it on 29 March 2024
Mmm, πz²a.
cook
This touched my brain in a very funny way
@@imveryangryitsnotbutter π is pi and z² is zz
This is a perfect example for kids in school asking when they will ever use math outside of school.
Yeah, except i can use a calculator sooo...
And except kids nowdays don't give a fck about the price or economy in general. The next Tik-tok video resets their worries...
@@deivisnxcalculator not useful if you don't know the formula...
@@KingAfrica4you don't even need to know the formula by heart, just that it exists and that it's applicable here
Pretty sure people wouldn't use this for pizza. Nobody is going to use math for that.
I am so sorry. I ate both pieces while attempting to solve.
😂
Which one took longer to eat? If you can determine that, we have ourselves an empirical solution.
@@perrinromney4555,
it'll always be the second i eat , just because it is the second , and because the difference between the volumes is rather small, as for my mouth .
@@keescanalfp5143 I disagree, I don't think the second one would be slower just because it's the second one for me
Everybody's out there doing actual maths and I'm here just counting the number of pieces of pepperoni and being objectively correct.
This is the only correct method
7" pizza has more pepperoni tho, but 6" pizza is more pizza per dollar.
Dont forget the pictures on display can be misleading.
The question is about which has better price to size ratio, not which slice is bigger. 7 inch pizza is larger but also costs more.
I just craft a glass bottle with those shapes and measure how many liters it takes to fill.
Bro has the quickswap skill unlocked for switching markers.
Since Pi is a common factor in the two areas, you can disregard that in the calculation and keep the maths easier.
1/360 is also a common factor that cancels out when you set up the ratio (also the units cancel out as long as they match, e.g. the ratio here is in square inches of pizza per square inch of pizza).
@@theodoremurdock9984 no, angle/360 does not cancel out.
One being 45/360 = 1/8
And the other 60/360 = 1/6
That leaves you with 49*(1/8)*pi
And 36*(1/6)*pi
Since pi is in both only another factor you can ingore pi
@@feuerschlange6374 nobody said anything about cancelling angle/360. They said that 1/360 is a common factor, which can be cancelled in both calculations.
i.e. 60pi×6² and 45pi×7²
However, the way I did it mentally was simplifying the fraction and expanding the square.
⅙pi×36 vs ⅛pi×49
pi can get cancelled
6 vs 49/8 = 6⅛
so the right one is slightly larger but proportionally much more expensive. So i estimated the left one is more worth it.
This would answer which is cheaper on a per area basis, but not tell you how much on a per area basis. But it wasn't asked so do it.
@@peterpan408so don't waste time on irrelevant calculations.
On paper, the first one is a better deal. But we cant forget that a larger angle means more crust. We should look at the ratio of crust to non crust as well.
Some people like more crust, especially if it’s stuffed.
@@russellharrell2747 absolutely fair. Still, crust to pizza ratio is definitely worth looking into.
Or dipping sauce
While I agree with your point that crust is an important consideration, I just want to point out that a larger angle doesn’t strictly mean more crust. Both angle and radius are a factor, but in this case, yes the 6in piece has more crust
@@russellharrell2747
Yep, I don't like the crust *_unless_* it is stuffed.
Like, I would eat it in a group situation, but if I have the choice, I’ll skip it.
I dunno man, you gotta consider the Crust Factor. The 1st Slice has a larger portion of the perimeter, thus more of a Crust/Cheese Ratio. Meanwhile, the 2nd Slice has less of a Crust Factor, and thus is appreciated at a higher value.
Don't forget the ergonomic aspect of pizza eating, its much easier and enjoyable to eat a thinner and longer slice
Crust is the best part.
@@Verxinnones worth is determined by their girth
Assuming a contant 1 inch wide crust of both pizzas, pizza #2 has a better cost to toppings area ratio!
@@vincentlamontagne7639 Euhmmm, no. I actually started out writing a comment exactly to this degree. But in fact the smaller pizza still has more area thanks to the larger angle. I was actually considering a partial value to the crust and was midway through the math when I decided to first check the basic math portion of it. Sooooo, I deleted the comment ;)
Real life example: Costco Pizza always have the best deal, very large, fairly affordable, and no need the hassle on figuring out which coupon to apply that provide the most mathematical and financial advantage.
Sure... Much like Ikea, they hope you leave with a good feeling about the food (Wow! That was a great deal!) so that it translates into a good feeling overall about shopping there. First impressions are important, but so are last impressions.
@@bokkenka I am still using my 15 year 70 inch desk from IKEA that was like $109 back then. The desk is still smooth and strong after moving like 5-8 times from house to house.
but you have to calculate the cost of an hour drive to get to a costco and the cost of the costco membership. math gets complicated.
@@johnpaullogan1365the deals and frequency and amount of stuff I buy more than justifies the car drive and membership. It's a no brainer...
@@johnpaullogan1365
those "members only" shops CAN be a good idea. if you go there often and buy a lot, because those small savings add up.
but if you dont buy a lot, it's mostly not worth it.
This is the type of question the teacher goes over in class that everyone loves and asks to be on the test.. then asks on the test as the final question “what width does the crust have to be for both pizzas (to the nearest quarter of an inch) for the deals to be equal for the cheese part?” .. simply to gauge if you truly understand what’s at stake in the original question.
I would love a video on how to figure this out please
The volume of a cylindrical pizza with radius Z and thickness A spells PIZZA.
Cut through the whole mess by never getting less than a whole pizza!
thats y you get like the $6 little ceaser pizza or something and you get to enjoy it yourself. 💀
Ooh. I like that thinking. Very creative
In this case you still have to be able to calculate whether a 24 cm diameter for 4 € is a better deal then the 28 cm diameter for 6 €!
And multiplying segment angle/360 is just one relatively easy additional step.
@@ailst That's all true, but you still end up with more pizza :)
@neilgerace355 The question isn't which pizza is bigger, the question is which is the better value. Three is bigger than one, of course. But which should you choose if given the option $1 each versus three for $5. The one, of course. 😅
Next time I see someone pull out a whiteboard while waiting in line to buy a slice, now I'll know why.
I've used a bit different method to solve this:
1. Divide the area for the bigger piece by the area of the smaller piece (pi's and 360's cancel out). I've got 45/60*(7^2)/(6^2) = 1.02 or 2% growth in area for the bigger piece.
2. Divide the prices: 1.70/1.50 = 1.13 or 13% growth in price for the bigger piece.
3. Since the growth in price is bigger than growth in area, smaller piece will be a better deal.
I just did 25 cents per inch and came up with 5 cent save for the 7 inch slice lol
@richard7199
You forgot that the 7 inch pizza is thinner.
With your logic a 10 by 1 rectangle of pizza is better than a 9 by 9 square of pizza.
@@mawillix2018 I never said we’d get more food from it, merely that we get more inches of pizza.
And you were wrong on both occasions. You aren't measuring length of pizza to determine what's better cost-wise, you use the volume (well, not exactly, we won't be able to properly calculate V, so S is fairly sufficient) @@richard7199
@@richard7199 That depends on how you measure the pizza.
Theoretically the thinner longer slice will be better since it will have less of that outer edge crust depending how much it takes up
Exactly! You have to take into account what portion of each is crust, cause everyone knows that cheesybites > crustybites.
This is exactly what I was thinking!
Not if you have dipping sauce for the crust
Similarly, when I compute the value of pizza, I subtract 1 inch from the radius due to the crust
outer edge crust is the best part. if you don't like it then you are a baby.
With just a couple of tricks you actually don't have to calculate exact values. First pizza has 36 square units for 9 bucks, so it's 4 units for $1. Second pizza has 49 units for 1.7*8 = $13.6, but for $13 we can buy 52 units of the first pizza. So, first is cheaper.
i did the same thing
My brain said, "bigger angle, not big difference in size, lower cost. Go with bigger for less cost."
No need for math.
I did something similar but I did some division so I had to use a calculator for the last bit. Using just multiplication is a lot nicer
The number of pieces does not take in account the diameter or radius of the individual pizza. The first has a diameter of 12, the second of 14, so the second might still be the better deal due to it being larger, thus to just count the pieces is not sufficent :)
@@gaia9020 I think you misunderstood Nomimasu's OP. Nomimasu spoke of _square unit_ which I think was a unit for surface area, i.e. square inch over pi. The numbers of calculation shown were acquired by filling up the discs & realizing that the surface area of a disc is proportional to the square of their radius a.w.a. that the constants that reappear in the expressions for both discs cancel each other out when comparing the two discs.
Now calculate how much more crust you are buying on the 6" slice.
Eat the crust!! 😅
the frust is good
That's the best part, that just improves the value of the 6' slice
The 60° slice has 8/7 times the crust of the 45° slice, which makes it better.
Assuming the crust is about 1 inch thick, the 6 inch slice has a better price per crust ratio AND a better topping per price ratio than the 7 inch slice.
49/36*6/8 = means second slice is 2% bigger but ~15% more expensive.
Yes, but 13 % more expensive.
But also less crust
Also more salami slices
Bread costs nothing but good pepperoni and cheese costs a lot.
Since you are only comparing the price/area of the two slices, pi cancels out and need not be calculated.
The 360 as well
But then you will only be determining the better value and not the specific values
Also the 360º in the denominator cancels out
@@msolec2000 I prefer to instead reduce the angles to 1/6 and 1/8. The areas then become 6(pi) and 49/8*(pi).
@@zeroone8800I did the same,so no need to approximate, which always introduce error
@@zeroone8800 Yes, and the of course pi goes away as well, which is a shame as I like pie as well as pizza.
I love your content, it is so good. It helps me so much since schools here aren't that great at teaching math
Love from Brazil ❤
es importante estudiar matematicas.
yo hago este tipo de computos siempre que hago la compra, porque a veces sale mejor comprar paquetes pequen~os que grandes, de la misma cosa y la misma marca....
You don't need to calculate the areas, just the ratio of 36/6 to 49/8. The latter shows the narrow slice is just barely larger, by a lesser factor than the price differential.
But you still need to consider the price factor.
Like so:
1.50/(36/6) vs 1.70/(49/8)
@@abacaabaca8131 or just check if 1.5*(49/8)/(36/6) is less than 1.7. simplifying gives us (3/2)*49/48) on the left side which is 147/96 which is 1.53125. so unless the second slice is less than that it is a worse deal
Yes, or compare 36*4, and 49*3, so 144 vs 147. Almost same area, while the difference in prices is much greater.
Yeah, this is simpler to compare with fractions and highlights why you need to be comfortable with using fractions and decimals. No need to calculate pi, save time to eat the pie.
Love this problem. Gave it to my students once and as a bonus had them calculate how long the pizza would have to be for them to get the same deal if the pizza was only 1° wide lol
I would love to eat a pizza like that. It would be like having a conveyor belt made of crust, which is carrying sauce, cheese and toppings into my mouth.
so a 1/2" radius pizza with a 45 degree arc? or a different radius and theta such that the length of the arc measures 1 inch but the area of that section of the pizza is such that it is 17/15 the area of the first?
If I were a student, i would have just said "it'd be more efficient to just weigh slices."
Seriously, by the time you solve this, the pizza done got cold.
when i figured it out, i just left pi out of the area equations. the ratio between the two areas is still the same with or without it, but it meant i was able to do it all without a calculator. well, except for the very end when i had to calculate 6.125 divided by 1.7
Thank you for the excellent content!
Gotta love unit pricing - VERY useful at the grocery store! In Australia the grocery has to show you the unit price on the shelf - EASY PEASY!
my grocery store does unit pricing but 3 brands of the same product one will give price per serving, one price per ounce and the 3rd will give price per gram
i do this all the time.
particularly when buying rice.
for some reason the larger packets of rice arent always cheaper per unit.
sometimes it's cheaper per unit to buy 2 small packets than a large one....so i always do the maths.....numbers dont lie. "common sense" does.
@johnpaullogan1365 clearly they hate customers by mixing up units.
Luckily in Australia the units match so the comparison is VERY easy to compare!
1st slice is 1/6 of a circle
2nd slice is 1/8 of a circle
surface area is pi*r^2
1st slice: 36pi/6 in^2
2nd slice: 49pi/8 in^2
now just make the bottoms the same to compare the sizes
288pi/48 in^2
294pi/48 in^2
seems like the 2nd pizza is better? well, it's bigger by about 2% but it's more expensive by 12-13%, so the first slice wins
unless you really hate the edge, then the 2nd pizza is better
In this particular example, as long as one knows that a circle is 360° in totality, one doesn't even necessarily need to know the (pi)(r^2) formula in order to figure out the solution.
60° = 1/6 of 360° and 45° = 1/8. 1/6 of the 6-inch-side is 1/1 (or 8/8), and 1/8 of the 7-inch side is 7/8. Now, without doing any (pi)(r^2) calculations, we can already see that they are selling the 8/8-proportion slice for $1.50 which is both larger (in proportion) and cheaper than the 7/8-proportion slice which is being sold for $1.70. So one doesn't even have to complete the extra-step of dividing the two different proportions by their correlating prices to know that the cheaper slice also has a larger area-for-cost-ratio making it the obvious choice for anyone who wants to "get more bang for their buck".
There are also other variables to consider, like the width of the crust, the overall thickness of the pizza slice, the weight of the toppings.
I'm disapointed that you didn't use a short cut to calculate it:
You don't have to calculate the /360 and the * π as they are both equal factors. So having to compare them you can just work with rational numbers:
6^2* 60 / 1.50 vs 7^2 * 45 / 1.70
That’s how I did it.
That makes the number bigger though, 1/6 and 1/8 is just easier
The /360 is easy to deal with here, it just factors out so it's 1/6 or 1/8 ... and that 1/6 further cancels against the 6^2
Im disappointed a double integral wasn't used to calculate the area
I'm glad we can instinctively tell that the 2nd one is slightly larger but not that large compared to the price difference
Humans are, generally, pretty bad at comparing tall and thin things with short and wide things. Though it's worse when dealing with volume since there's an extra dimension involved.
i couldnt instinctively tell. i had to do the calculations.
i dont trust "instincts" or "common sense". i trust numbers.
As a lot of people here have pointed out, the crust is also important. In addition to that, the enjoynment of the crust matters too. Lets label that 'c'. The enjoynment of the rest would be 1 as in 100 %. Assume that the crust is 1 inch.
The wide pizza has an area of
A_wp = 1/6*π*5^2 = 25π/6
and the tall pizza has an area of
A_tp = 1/8*π*6^2 = 9π/2
Crust is the remaining area. For the wide
A_wc = 1/6*π*6^2 - 25π/6 = 11π/6
and for the tall
A_tc = 1/8*π*7^2 - 36π/8 = 13π/8
Total food/enjoynment you're getting is
f_w = (25+11c)/6
f_t = (36+13c)/8
Calculating the price per dollar for each gives us
p_w = (25+11c)/6/1.5 = (25+11c)/9
p_t = (36+13c)/8/1.7 = (36+13c)5/68
Finally, lets see how much the crust enjoynment needs to be for each choice.
(25+11c)/9 = (36+13c)5/68
68(25+11c) = 45(36+13c)
1700+748c = 1620+585c
80+163c = 0
c = -80/163 ~ -0.49
As we see, since the enjoynment needs to be a negative number (0 means no crust basically) so regardless of whether you like crust or not, you should get the wide piece.
Proud that I worked this exactly the same way before watching it. I worry about forgetting things as I age, I'm happy to report I may not use it as much as I would like, but I still can!
I dunno. The 2nd pizza has more pepperoni.
That's why it is 20 cents higher
of course it has more pepperoni, the total area is larger. the question is meant to measure value not absolute amounts
Can you teach how to do the instant marker-swap techinique? Does it work with pens aswell?
Type "how to blackpenredpen" in the search bar
It does, you just need to rotate it, u just use your index finger to push and use the one above.
Well at least that's how i do it , i think there's different method of doing it since i just try to copy my friends long ago
@@inmuyataz a video tutorial would be nice for that
@@alexzaze1407 He already has a video about it: th-cam.com/users/shortsgoMm-zD4tKA
@@alexzaze1407 He already has a shorts video about it. Search "how to blackpenredpen"
This was the most important math problem i needed to learn. Thank you!
it took me to tries to figure this out. first i wondered computing just the area of a slice, but since it's not exactly a triangle, that got complicated fairly quickly, i considered just ignoring the arched part, but then i thought of your method, using the radius and angle to compute the area based on the entire pizza.
i agree with your result. and your analysis. and thus left a like and this comment.
keep spreading maths. the world is a tiny bit better for your efforts.
Now let's add the thickness. If the first pizza slice is 'thin and crispy' with thickness of 3/8 inch and the second is 'deep dish' with thickness of 1 inch.... lol
Yeah thickness is important as well
why not include the toppings count and crust width at the edges
this and crispy will ALWAYS lose to total amount of pizza per price haha. it's like a cracker with sauce and cheese. but it's never any cheaper than hand tossed crust
We were talking about Pizza here, deep dish is a garnished bread or tomato soup in a bread bowl, depending where you buy it, but not a pizza. :D
@@h4z4rd1000exactly. Thickness affects the deliciousness factor.
Actually, it did, but not in the way you might think. 6" slice has 7.5 pieces of pepperoni @ cost of $1.50. 7" slice has 8.75 pieces of pepperoni @ $1.70: 6" = $1.5/7.5 = $0.20 per slice of pepperoni, 7" = $1.7/8.75 =$0.19 per slice of pepperoni...7" slice is more cost effective at a penny less per slice of pepperoni. Cost of making pizza [manhours] is same regardless, cheese & sauce are fairly comparable across the two; pepperoni is most expensive ingredient on the pie. 8) Area of slice may be larger, but you're getting a more expensive meat topping.
i would say it is only 8.5 slices on the 7" - so value for that, but everything else is more.
@@ABaumstumpf Point [tongue-in-cheek] was meant to show there's more to the calculus than sheer geometry; otherwise agreed. 8)
that's fine if all you care about is maximizing total pepperoni. but that is obvious to see since the 2nd one has a larger total area. some of us prefer more crust so the first one wins in both price per unit area as well as more crust
I ran that into the triangle calculator. First slice has an area of around 15.5 and second 17.2. If you divide that with the price you get around a factor of 10 for both but you get slightly more with the first.
You can vastly simplify since in calculating the area, pi is a common factor. Just square the length and divide by the number of slices you could slice (60 is 6 slices, 45 is 8 slices). You don't even have to consider price at that point because it will be apparent that the 7in pizza has marginally greater area but costs a lot more.
Calculator isn't necessary to compare both since both share the factor of pi/360° which you can ignore and compute the rest
That is why sellers of pizza never gives you mathematical data for you to buy it in the wrong way
Hahaha
I simply figured how much each pizza would cost once you added each slice to equal 360*.
A) 1.50 x 6 =$9
B) 1.70 X 8 = $13.60
Knowing that two more slices of A would still be less costly than B. However, if B was better quality and taste and there were only two people sharing the pizza B would be the better choice. Simply based on shared experience.
It's cool that just looking with my eyes I could make the correct guess that the left slice was a better deal. There is also the factor of edge crust vs toppings, but it's not enough in this case to make the larger slice better.
I somehow decided to just use my math skills while lying in bed with post nut clarity. It felt nice to do math
Play a game of chess before you sleep, it's fun to use your brain before sleeping.
@@davidsantiago7808 then you lose without knowing why to someone who won without knowing why.
then it didnt matter and now its the morning and your thinking about life after what ever occurs in the day.
@@PoKeKidMPK1 or u win, but either way you experience a fun way to work the brain. Unless you're a sore loser you coudl have fun even if you lose, chess is just a game after all. The brain is a muscle, and a lot of people lack hobbies that stretch the brain. I am just saying it is healthy and relevant to the original comment
@@davidsantiago7808 i dont think you do activities like chess often. it doesnt work that way, in even basic actions. googling info like that doesnt either because it creates beliefs.
internet/supplements vs common good habits and purposeful testing
worrying about being glorified on a random nights single chess game is also a hilarious self-brought contradiction to the point of learning.
@@davidsantiago7808 you must not do activities like chess often then. it doesnt work that way, in even basic actions. you mind as well tell him to wake up, walk, breath, live life and it would be the same redundant idea. searching info like that doesnt either because it creates a fantasy.
internet/supplements vs common good habits and purposeful testing
worrying about whos being glorified on a random nights single chess game is also a hilarious self-brought contradiction to the point of learning.
So good! As soon as I though of pizza I couldn't stop watching
Will be teaching this to my kids!
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Can I also do it??? My life is facing lots of challenges lately
If this was how teacher teach math at school i would have been a math wizard
So interesting that you worked this out as $/in² when I would've never thought to express the cost as anything other than in²/$.
"Okay, okay, what's better? A medium amount of good pizza? Or all you can eat of pretty good pizza?"
holding on to pi until the final step is always more satisfying
"ah, but what of the crust-to-pie ratio?" me at 4am
This is important.
plus as a high school dropout with terrible math skills, but knows pizza, the 60 degree cut will yield more crust per $/ square inch vs the 7 inch slice at 45 degrees.
I use this same math to calculate “sale” prices versus regular prices at a grocery store.
Took me a second to realize you have two markers in your hand. I though it was a magic marker! 😂
a great way to simpify pi calculations, is to treat pi like an unknown, and just leave pi as it is.
1st slice = 60/360 x pi x 6²
= 1/6 x 36 x pi
= 6 pi in²
2nd slice = 45/360 x pi x 7²
= 1/8 x 49 x pi
= 6.125 pi in²
then calculate price per area, $1.50 is same as 150 cents (the answer is gonna be cents anyway so this helps you understand easier)
so 150/6 pi = 25/pi cents per square inch
170/6.125 pi = 27.755/pi cents per square inch
even without calculating pi = 3.14159..... you already know which one is is cheaper
initial thought: pi * r^2, divide by 360 over the angle, then divide by the price to get square inches per dollar
(this was breifly covered in my pre calc class)
I really like this problem because it also offers you a good stepping stone into multivariates. You can figure out the ratio between slice angle and Pizza radius to figure out a general formula for computing the best deal. Very fun stuff!
Quick mental maths, area proportional to radius squared * fraction of the circle, and I just divide by the price to find smin related to area/dollar
6^2*1/6 = 6; 6/1.5$ = 4
7^2*1/8 = 6.125; 6.125/1.7 is less than 4 (1.7*4 = 6.8)
first option better (I am indeed an engineering student)
I did it the same way. I've been an engineer for 40 years.
hi dude, I know its the wrong channel, but thanks to your linear differential equation video series, I got 92.5% on my calculus 1 final! Thank you so much for making math fun and showing me that even higher level stuff can be fun if its presented in that way! Cheers!
*goes into pizza shop*
“Yeah I’d like to get a slice of pepperoni.”
*whips out tape measure and protractor*
This is a pretty simple problem. But definitely makes students care more lol. The long pizza is larger but you get more pizza per money on the wide one.
I just used radius to calculate area of a circle, divide it based on the angle and then use that to divide the cost.
Angle of the second pizza is 3/4 the size of the first one. You dont need pi, just that the radius is squared, so we're comparing 6² with 3/4*7², which is 36 and 36.75. divide by the cost to find the actual value. 24 arbitrary value units for the first pizza, and roughly 21.6 for the second
Here in Brazil, in the National High School Exam (our s.a.t), we have a lot of these type of questions in the math section, so when this video showed up in my recomendations I already knew what I had to do to get the answer. Math is really usefull when it comes to buying or at the restaurant, now when I go to the pizza place I always calculate the price by area, my girlfriend hates it hahah.
60° makes up 1/6th of 360. Find the area of a circle with a radius of 6 inches and then divide by 6.
45° makes up 1/8th of a circle. The radius is now 7 inches.
In the time it took you to figure that out, your pizza was getting cold.
see this is a good math teacher, it all makes sense, down to the marker colors, red = variable, black = constant
Regarding the crust. If the crust is longer than ~ 1.6 Inches then the tall one would be cheaper
My math is how many pieces of pepperoni am I getting over the other one. Which ever one has more I'm buying.
From a Programming side, I recomment to see if you are comparing two values that requires Pi to find then leave the Pi to the end and see if you can ignore Pi. The goal is not to find the cost per area and to find the smaller cost per area.
So the 60 degrees slice would be (1.50/6 or 0.25) * 1 / Pi and 45 Degree slice become (1.70 / 6.125 or 0 .27755) * 1/Pi since Pi is constant you just need to pick the smaller number which is 60 degree slice with 0.25 * 1/Pi.
Videos like these are great for testing whether we can do math still. I always try to solve and se how you did it differently. In this case my units were in^2pizza/$ because I'm doing math with my stomach today, not my wallet. This is why units matter!
I think comparing the area per unit currency would have been a more intuitive way to compare the two, but this works too of course!
The $1.70 has less crust and looks like more pepperoni slices in thumbnail, that's additional value
You don't need to think about the value of Pi when you're comparing two values like this. The volume of the slice on the left is 60*6^2*(some constant). The volume of the slice on the right is 45*7^2*(that same constant). Divide both sides by the unknown constant, divide both sides again by 15 degrees, and you come up with the very easy comparison between 4*6^2 and 3*7^2. You can do that in your head.
Since pi is in both areas, it may be helpful to consider it as part of the units. Assuming I did my math right, I found slice a to have an area of 6 pi in^2 and slice b to have an are of 6.125 pi in^2. Considering the price per slice, that resulted in $0.25 per pi square inches for slice a and about $0.28 per pi square inches of slice b which seem like more useful numbers in this context
Just buy and eat, damn it! I’m hungry ! 😂😂😂
Yeah I just looked at it for like 2 seconds and could tell, and also recognize that they were very close in value.
This is just area; Total volume or weight, even, could change things completely
Another thing to consider, specifically for pizza, the 6" slice has more edge and thus less toppings and sauce.
The thing is medium and large pizza usually use same amount of dough, so medium is thicker and large is thinner
And the thinner one usually taste better
Not true @Domino's.
These are the examples needed to teach math to students.
It helps them understand a better deal, something they'll likely want to know. Plus, pizza.
The Area of a circle: A(circle) = pi * r^2
A full Circle with 360° = 1 => 45° and 60° are 0.125 (45/360) and 0.1667 (60/360)
Let pi approximately equal 3.14159
A(60° & 6in) = 3.14159 * 36 * 0.1667 = 18.85
A(45° & 7in) = 3.14159 * 49 * 0.125 = 19.24
Area of respective pizza divided by respective cost:
18.85 / 1.5 = 12.5667
19.24 / 1.7 = 11.32
=> You get ~11% (12.5667 / 11.32) more surface area per dollar if you choose the 60°, 6-inch pizza slice versus the 45°, 7-inch slice.
You can also divide the area by the price to find the amount per dollar
Another neat approach to this is to look at scale factor.
The 60deg pizza is, 60/45 x 36/49 times bigger/smaller than the 45deg pizza. (smaller) Which comes out at about 2.08% less area.
But the price of the smaller pizza is 13.33% cheaper. In other words, the 45deg pizza, costs 13.33% more currency, for only 2.08% more area.
This is great! I've used pizza math before when considering a local shop's two large pizzas (round) vs. one "colossal" pizza (square). *note, the colossal was a better deal! LOL. And yes, my wife thought I was nuts, but hey, I'm the math nerd in the family so what do you expect....
As the area of a circular sector grows linearly in the angle and quadratically in the radius, you can see that the second slice would have to cost 1.50*(45/60)*(7/6)^2 = $1.53, but it costs more so the first one is better value.
You saved my life, thanks
“OP did not mention, the 1.50 pizza uses cheese processed with almond milk from North Korea, whereas the 1.70 pizza uses marinara sauce made with soy from Taiwan.”
Man, im just getting both of them
My stomach says that both of them are a better deal. 😅 Thanks for a good video.
Just like high-school I quit paying attention pretty much right away and just waited for the answer. The original thought was the $1.50 slice
My math was a little more rough, and I was looking for different values. I calculated that the 7-inch piece gives you 2% more pizza for a 13% price increase.
(7^(2)÷8)÷(6^(2)÷6) ≈ 1.021, so the long slice is aproximatly 2.1% bigger, but the price, is way bigger than that so i'd choose the phat slice.
Area of a sector is proportional to radius squared and the angle. The units don't matter if we are just making a comparison.
So 6 * 6 * 60 / 1.5 = 1440 area units per dollar
And 7 * 7 * 45 / 1.7 = 1297 area units per dollar
The first one is better value and it doesn't take almost 5 minutes to work out.
The first thing I do at the slice shop is bust out my protractor. Slice shop owners hate this one trick.
I think the teacher wanted the answer with pi as a factor and using the unit square inches per dollar, because then the first slice would be 4πin²/$ against ~3.6πin²/$.
Funny, I've seen something similar at my local supermarket. I think they set the price based on the radius of the pizza, which means the bigger ones are much better value!
The secret is that you want to be the one that offers both of these deals and let me explain why
if a customer sees two deals they instinctively focus on which one is the better deal and then decide which one to buy. this automatically puts both deals in contrast and the customer will be more tolerant towards the deal that is "better", disregarding that they could potentially be ripped off no matter which one of them they buy because they could both just be overpriced.
As the one who offers both of these, you can just make both of them overpriced but one a little cheaper than the other one and profit.
Also, it seems to me that the probability of getting more toppings per sq. in. is higher with the 6" radius piece as well. :)
Great example.