A water tank consists of a cylindrical part of radius r and height h, and a hemispherical top. The tank is to be constructed to hold 500 m3 of fluid when filled. The surface area of the cylindrical part is 2πrh, and its volume is πr2h. The surface area of the hemispherical top is given by 2πr2, and its volume is given by 2πr3/3. The cost to construct the cylindrical part of the tank is $300/m2 of surface area; the hemispherical part costs $400/m2. Plot the cost versus r for 2 ≤ r ≤ 10 m, and determine the radius that results in the least cost. Compute the corresponding height h.
