Question

Three friends want to share a circular 12-inch pizza equally by
exactly only two parallel cuts. How far from the center must the
cuts be? Hint: The pizza is a circle of radius 6 inches.

Answer 1

If the cuts are at a distance of x from the center, then since the area of a circular segment is

a = 1/2 r^2(θ-sinθ)

we want that to be 1/3 of the area, or π/3 r^2

So,

1/2 r^2(θ-sinθ) = π/3 r^2
3(θ-sinθ) = 2π
Solve that using your favorite method, and we have
θ = 2.6

So, x/r = cos θ/2
x = 1.6 in from the center

Answer 2

sadaf