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91Ó°ÊÓ

Find the work described in each of Exercises 49–60.

The work required to pump all of the water out of the top of a giant rectangular hot tub that is 5 feet wide, 8 feet long, and 3 feet deep.

Short Answer

Expert verified

Required work is 11,232 foot-pounds.

Step by step solution

01

Given Information 

The work required to pump all of the water out of the top of a giant rectangular hot tub that is 5 feet wide, 8 feet long, and 3 feet deep.

02

Slice representation 

Hot tub is 3 feet deep. Height of the tank is y=3 and bottom is y=0

Width of the slice is delta y or y_k

Slice at y needs to be removed upward is

3-yk

03

Volume  and Work 

Volume of tub= length times width times height

Tub is 5 feet wide, 8 feet long and change in width is delta y

V=5*8*∆yV=40∆yWorkrequiredformulaW=Fd=ӬVdWaterdensity=62.4poundsperfootd=3-ykW=(62.4)(40∆y)3-yk

04

Integration 

Work required to pull out the water completely is the sum of the slices from y=0 to 3

W=(62.4)(40∆y)3-ykW=∫03(62.4)(40)3-ydy=2496∫033-ydy=24963y-y2203=24963(3)-322=11232

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