An open topped taking tin with a volume of 864 cm is to be constructed with a square base and vertical sides. Find the least amount of tin plate required.

Answer 1

if the base has side x and the tin has height y, then

x^2 y = 864
y = 864/x^2

The surface area a is

a = x^2 + 4xy = x^2 + 4x(864/x^2)
= x^2 + 3456/x

da/dx = 2x - 3456/x^2
= (2x^3-3456)/x^2
da/dx=0 when x=12.

Now find the area.