The most economical tin can to manufacture is one that is a right circular with height equal to twice the radius. one such can has a volume of 54 pi cm cubed. what is the total surface area of this can in cm squared?
Vol =pi(r^2)(2r) = 54pi
so 2r^3pi = 54pi
r^3 = 27
r = 3
the surface area is made up of 2 circles plus a rectangle with height 2r and length 2pir
rectangle = 2pi(r)(2r) = 4pi(r^2)
the 2 cirlces have area of 2pi(r^2)
so the total area = 6p(r^2)
= 6pi(9) = 54pi cm^2