Quonset huts were developed during World War II. They were temporary housing structures that could be assembled quickly and easily. A Quonset hut is shaped like a half cylinder. A manufacturer has 600 square feet of material with which to build a Quonset hut.
(a) The formula for the surface area of half a cylinder is S = r2 + rl, where r is the radius and l is the length of the hut. Solve this equation for l when S = 600.
(b) The formula for the volume of the hut is V = 1/2(r2l. Write the volume V of the Quonset hut as a polynomial function of r.
(c) Use the function you wrote in part (b) to find the maximum volume of a Quonset hut with a surface area of 600 square feet. What are the dimensions of the hut?