Can you find the blue area? |
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- เผยแพร่เมื่อ 11 พ.ย. 2024
- Can you find the blue area? Watch the video to see my solution! Did you get the same answer? Was your solution different to mine? Let me know in the comments below!
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Thanks for your comment, glad you enjoy 😀
Wow, that was pretty breezy! I solved it a bit differently. I rotated the whole figure 45 degrees, and put it on an x-y plane centered at the center of the figure. I then found a formula for the blue circle and for the quarter circle centered at the bottom of the (now) diamond. Those are:
y = sqrt(25 - x^2) and y = sqrt(100 - x^2) - sqrt(50)
I solved that system of equations to figure out where they cross (on the right), at x=5 sqrt(14)/4.
Then I set up the integral to find the area between those two graphs over the range x=0 to x=5 sqrt(14)/4, which gives a quarter of the total blue area. Multiply by 4 to get 29.276.
Sure, I plugged the integral into Wolfram Alpha, but if we're just looking for a numerical answer, that's good enough, right?
Nice solution!! I’ll talk a bit slower next video 😀
@@mrtalbotmaths Haha awesome!