A gardener is building a shed to protect his plants from hot weather. Its shape is the surface of a half cylinder with radius r and length h as shown. The material needed for the two flat semi-circular ends costs 10 dollars per square foot. The material needed for the upper curved portion costs 4 dollars per square foot. A bottom will not be needed.

A gardener is building a shed to protect his plants From hot weather. Its shape is the surface of a half cylinder with radius r and length h as shown. The material needed for the two at semi-circular ends costs 10 dollars per square foot. The material needed for the upper curved portion costs 4 dollars per square foot. A bottom will not be needed. ,, P (a) Find the total cost, C(r) , for building this shed as a function of the radius if the volume inside must be 200 cubic feet. 0 CU) : m2 + 200 J" 0 Cir) = m2 + 16:10 O CH) : mm; + 16:10 0 Cir) = 5M2 + g 0 C(r) : 20ng + lroo 200 0 CU) : 10er + T (c) Find the exact value of the radius of the shed that minimizes the total cost. r = ' -Select 0