Question

A cylindrical can with a volume of 125m³ (about 2 litres) is to be made by cutting its top and bottom from metal squares and forming its curved side by bending a rectangular sheet of metal to match its ends. What radius ‘r’ and height ‘h’ of the can will minimize the amount of material required.

Answer 1

The circular top and bottom should be cut out from a square metal sheet of side 2r. Therefore the area of squares is 8r².

Area A = 8r² + 2πrh

∴ To minimize the amount of material, r = 2.5

h = \(\frac{125}{π(2.5)^2}\) = 6.3.