(793,#31) Use differentials to estimate the amount of tin

(793,#31) Use differentials to estimate the amount of tin in a closed tin can with a diameter 8 cm and height 12cm if the tin is 0.04 cm thick.
Solution:

Volume of a cylinder(tin can)
where r = radius = 4cm
h = height = 12cm
Applying the definition of the differential dz,

The differential of V is:

Suppose that the radius is decreased by 0.04 cm (dr = -0.04) and the height is decreased by 0,08 cm
(dh = - 0.08). Then
dV = 96 Pi (-0.04) + 16 Pi (-0.08) = 16.08
This difference in volumes represents the space occupied by the tin of the can.
Thus the amount of tin is approximately
No Maple Code for this problem.

by: sh