Question

A farmer wishes to paint the side of a cylindrical grain silo of height 60 feet and diameter 24 feet. If the paint is to be applied in a coat 1/8 inch thick, use differentials to approximate the volume of paint that the farmer needs to buy.

I calculated that to be 15pi ft^3
It then asked for the actual error in approximation which i got to be 0.0205 ft^3

What is the relative error when compared to actual volume of paint required? (Round your answer to six decimal places.)
this i don't know how to solve

Answer 1

to solve the volume of the paint the farmer will need, calculate the volume of the silo by using a diameter plus the thickness of the paint, the substract it with the actual volume

Volume paint = 60(( 24 + (1/8)(1/12) )/2 )^2 - 60(( 24 )/2 )^2
volume paint = 23.58 cubic ft is the required volume