A hemispherical dome of radius 40 feet is to be given 11 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 40 feet to 40 feet 11/100 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 11 coats of paint.

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