Is there a formula for this?

Question

My frugal friends Bob and Tom love pizza; Bob the edge pieces and Tom the center pieces. Is there a formula to figure out how to cut a circular pizza so that they both get the same amount of pizza while getting their preference?

Answer 1

Assume a pizza of radius R.

The area of that pizza is pi*R^2.

To find the radius of the inner circle (r) to cut use this equation

(1/2)*pi*R^2 = pi*r^2

r^2 = (1/2) * R^2
r = sqrt ( (1/2) * R^2 )

Cut a circle in the pizza of small radius r in order to get the same amount of pizza.

Answer 2

my guess is make a square pizza with dimensions 8 by 8. that way there are 64 pieces total. add the outsides, 8+8+8+8 and you get 32, which is half the pizza. i'm not a formula guy, so you do the rest

Answer 3

First find the area of the whole pizza, then divide by two and find the radius at which it needs to be cut to get two sections with equal area. ( a circle within a circle.)

square root of: ((Area / 2) / π)

will give you the radius of the circle that must be cut.

Answer 4

Let's say there will be two radii for the circular pizza to be sliced according to them, the first one one is R1 which is the actual radius for the pizza and the second one is R2 which is unknown.. the equation will be: (pi)(R1)^2 - (pi)(R2)^2 = (pi)(R2)^2 [pi=3.14159265358979323846].. Which is, the area of the inner circle is equal to the area of the outter one.
bon appétit..