Maximizing the Volume The volume of the cup in Exercise 115 is zero if α is 0° or 36...

Maximizing the Volume The volume of the cup in Exercise 115 is zero if α is 0° or 360°. Somewhere in between the volume reaches a maximum.

a. Use the maximum feature of a graphing calculator to find the angle α to the nearest hundredth of a degree that gives the maximum volume for the cup.

b. What is the maximum volume for the cup to the nearest tenth of a cubic inch?

Exercise 115:

Volume of a Cup Sunbelt Paper Products makes conical paper cups by cutting a 4-in. circular piece of paper on the radius and overlapping the paper by an angle α as shown in the figure.

a. Find the volume of the cup to the nearest tenth of a cubic inch if α = 30°.

b. Write the volume of the cup as a function of α.