In this question you are required to design a cylindrical tank with a capacity of 36 m ³ , while minimising the cost. The tank will have an open top, and can be at most 6 m high. The material for the base costs $10 per m ² , while the material for the sides costs $5 per m ² . The goal is to find the radius r and height h of the tank that minimises the cost C , and the cost itself. 

a. Draw the tank and label the dimensions.

b. Write down an expression for the cost C in terms of r and h initially, then use the constraint on the tank capacity to express C in terms of a single variable. Either r or h may be used, but one may be easier to use than the other.