Question

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower = 550 ft-lb of work per second.)

Name: Problem 22, Chapter 6: Calculus: Early Transcendentals
Uploaded: 2019-06-23T14:52:31-08:00
Duration: 2 min 41 s
Channel: Yiming Zhang

   Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower = 550 ft-lb of work per second.)

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 6, Problem 22

Instant Answer

Solved by Expert Yiming Zhang

06/23/2019

Step 1

We are looking for the time, so we rearrange the formula to get time equals work divided by power. Show more…

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Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower = 550 ft-lb of work per second.)