Question

Use differentials to estimate the amount of material in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.05 cm thick.

Answer 1

dv = attached below

dr = 0.05 cm

dh = 0.2 cm

Approximate volume of metal = 2.8 * π cm^3

Explanation:

height of can ( h ) = 10 cm

diameter = 4 cm ; r = 4/2 = 2cm

thickness of metal in top and bottom = 0.1 cm

thickness of metal in sides = 0.05 cm

attached below is the detailed solution