Question 314888: I have a pizza. The radius is 10 inches long. The pizza was cut into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.
1. Find the area of the whole pizza.
a=(pi)(10^2), =314
2. What is the area of one piece of pizza?
(pi)(r^2)/16, 100(pi)/16=19.6
3. What is the area of a half-piece?
100(pi)/36=10
4. What would the area of the whole pizza be if it were made of half pieces?
a=10(pi), a=100/10, a=10
5. What is the radius of a half-piece? (ie, where do I need to cut to make two equal halves out of a piece?)
I was wondering if I got these answers correct. If I did not, could someone please explain what I did wrong?Also, I was a little confused as to how to get the answer to the last question. Cheers!
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! 1. Find the area of the whole pizza.
a=(pi)(10^2), =314
2. What is the area of one piece of pizza?
(pi)(r^2)/16, 100(pi)/16=19.625
3. What is the area of a half-piece?
100(pi)/36=10 (9.8125 ans.)
4. What would the area of the whole pizza be if it were made of half pieces?
a=10(pi), a=100/10, a=10 (9.8125 ans)
5. What is the radius of a half-piece? (ie, where do I need to cut to make two equal halves out of a piece?)
What you have is an isosoeles triangl with 2 side=10 and the included angle=22,5.
Area=1/2x*x+sin 22.5
9.8125=x^2/2*.383
9.8125=x*2*.1915
x^2=9.8125/.1915
x^2=51.24
x=sqrt51.24
x=7.158 inches from the point is where the cut will half the piece.
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