Homework Help: Geometry

Posted by Kathy on Wednesday, June 30, 2010 at 9:12am.

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!

Geometry - Reiny, Wednesday, June 30, 2010 at 9:28am
I agree with 1. and 2.

In 3.
why are you dividing by 36.
If by the "area of a half-piece" you mean half the area of one of the 16 slices, then it would be
100π/32

I do not understand question #4

5. I will assume that your cut will be an arc.
so let the radius of that small piece be r
so πr^2 = (1/2)(19.6)
r = √(9.82/π) = 1.77 inches

If your cut is a straight line such that the smaller piece is an isosceles triangle, then the question would be a bit more difficult.
Geometry - Reiny, Wednesday, June 30, 2010 at 9:35am
My answer to #5 is wrong,
go with bobpursley's way
Correction - Geometry - Reiny, Wednesday, June 30, 2010 at 9:39am
in #5
I will assume that your cut will be an arc.
so let the radius of that small piece be r
so πr^2/16 = (1/2)(19.6)
r = 7.1 inches

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