Hyungmin designs a concrete bird bath. The bird bath is

Last updated: 7/10/2022

Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal. This is shown in the diagram below. The interior of the bird bath is in the shape of a cone with radius r, and height h and constant slant height of 50 cm. a) Write down an equation in r and h that shows this information. Let V be the volume of the bird bath. Hyungmin wants the bird bath to have maximum volume. b) Show that V = 2500πh/3-πh^3/3. c) Find dV/dh d) Use your answer in part c to find the value of h for which V is a maximum. e) Find the maximum volume of the bird bath f) To prevent leaks, a sealant is applied to the interior surface of the bird bath. Find the surface area to be covered by the sealant, given that the bird bath has maximum volume.