Question

A hemispherical dome of radius 50 feet is to be given 3 coats of paint, each of which is 1/100 inch thick. Use linear approximation to estimate the volume of paint needed for the job.

( Hint: Approximate the change in the volume of a hemisphere when the radius increases from 50 feet to 50 feet 3/100 inches. Don't forget to make sure this increased radius is in terms of feet. )

It will take approximately  cubic feet of paint to apply all 3 coats of paint.

Answer 1

solution:

The volume of the hemispherical dome is

Differentiate both sides w.r.t r

Therefore,

Approximate the volume change as

i)

For the hemispherical dome with paint upon it

Therefore, Volume of paint needed in 3 coats is the change in volume of the hemisphere and is given by

Numerically

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