Question

A cylindrical can, open at one end, is to be made out of aluminium.

a) If the surface area of the can is to be 200 cm^2, find an expression for the height, h, of the can in terms of the radius, r.

b) Find a function for the volume, V, of the can in terms of the radius, r.

c ) Find dV/dr.

d) Hence, find the exact value of the radius that gives the maximum volume of the can. Give the radius correct to 2 decimal places.

e) Find the volume of the can both in exact form and to the nearest cm^3.