Question

A hemispherical dome with radius=20 feet needs 11 coats of paint, which are 1/100 inch thick...need to use linear approximation to get the volume of paint needed for the job.

Answer 1

Using linear transformation to get the volume the volume we can use the following formula

V = (2/3) x pi x r^3

40 ft .11 inches = 480.11 inches
Putting in the formula we getV = (2/3) x pi x (480.11^3 - 480^3)

V = (2/3) x pi x 76049.4 inches V = 159277.54 inches
There are 1728 cubic inches in 1 cubic foot
V = 92.17 cubic feet