a slice of pizza, in the form of a sector of a circle, is to have a perimeter of 24 inches. What should be the radius of the pan to make the slice of pizza largest?

Answer 1

let the arclength of the sector be a
then 2r + a = 24
a = 24-2r

Let the area of the sector be A
then A/(πr^2) = a/(2πr)
A = a(πr^2)/(2πr)
= ar/2
= (24-2r)r/2
A = 12r - r^2
dA/dr = 12 - 2r
= 0 for a max of A
12-2r = 0
r = 6