Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and the bottom is 0.3 cm thick and the metal in the sides is 0.05 cm thick.

The volume of metal in a can is 13.8 cm³.

Explanation:

Given that,

Height = 10 cm

Diameter = 4 cm

Thickness at bottom = 0.3 cm

Thickness at side = 0.05 cm

The change in radius = 0.05 cm

The total change in height is

The volume V of a cylinder in term of height and radius r

Using formula of volume

On differentiated with respect to r

...(I)

On differentiated with respect to h

The total differentialis,

Put the value into the formula

Put the value into the formula

Hence, The volume of metal in a can is 13.8 cm³.