## Calculus: Early Transcendentals 8th Edition

The diameter should be $~~16~in$
Let $\theta$ be the central angle of the pizza slice. Let $r$ be the radius of the pizza. We can use the perimeter to find an expression for $\theta$: $r+r+\theta~r = 32$ $\theta = \frac{32-2r}{r}$ We can find an expression for the area of the pizza slice: $A = (\frac{\theta}{2\pi})~\pi~r^2$ $A = \frac{\theta~r^2}{2}$ $A = \frac{(32-2r)~r^2}{2r}$ $A = (16-r)~r$ $A = 16r-r^2$ We can find $\frac{dA}{dr}$: $\frac{dA}{dr} = 16-2r = 0$ $r = 8$ Since the diameter is twice the radius, the diameter should be $~~16~in$