Using differentials to approximate things. A farmer wishes to paint the side of

Question

Using differentials to approximate things.

A farmer wishes to paint the side of a cylindrical grain silo of height 65 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. ______ft3 Calculate the actual error in the approximation. ______ft3 What is the relative error when compared to actual volume of paint required? (Round your answer to six decimal places.) Using differentials to approximate things.

Explanation / Answer

The silo itself is a cylinder of radius 12 ft and height 65 ft, whereas when painted the radius is increased to [12 + 1/(8*12)] ft. The volume Vo of the paint required is therefore given exactly by the difference in the volumes of these two cylinders

Vo = 65*?*(12 + 1/96)

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