If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 28 inches, what diameter pizza will reward you with the largest slice

The diameter that will reward with the largest pizza is 14 in

Step-by-step explanation:

The perimeter of a sector of a circle is:

P = 2r + l

l = rθ

P = 2r + rθ

P=28 inches

28=2r + rθ

28-2r=rθ

θ=(28-2r/r)

=(2*14 - 2*r)/r

=2(14-r)/r

Area of the sector of the circle is:

A = r²/2 * θ

A = r²/2 * 2(14 - r)/r

A = r² * (14 - r)/r

A = r(14 - r)

A = 14r - r²

For the maximum area:

A = 14r - r²

A' = 14 - 2r

Set A' = 0

14 - 2r = 0

14= 2r

r = 7 in

The diameter (D) of the circle is twice of the radius:

D = 2r = 2 * 7= 14 in

The maximum area is:

A = 14r - r²

r = 7 in

A = 14 * 7 - 7²

A = 98 - 49

A = 49 in²