A tank in the shape of a sphere of radius 9 ft is full of water. Find a single integral whose value is the work done when the tank is emptied by pumping all of the water through a spigot located at the top of the tank. Use the fact that water weights 62.5 lb/ft3. Do not evaluate the integral.

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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 A tank in the shape of a sphere of radius 9 ft is full of water. Find a single integral whose value is the work done when the tank is emptied by pumping all of the water through a spigot located at the top of the tank. Use the fact that water weights 62.5 lb/ft3. Do not evaluate the integral.

Expert Solution
Step 1

The radius of the sphere is 9ft.

The weight of water is 62.5 lb/ft3.

Step 2

Consider a circular layer of the sphere tank.

The radius if the circular layer is calculated as,

r=92-y2

The volume of the circular layer is,

Vcircular layer=πr2dy=π81-y22dy=π81-y2dy

The weight of the layer is,

wlayer=62.5×π81-y2dy

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