This is a two part question that I do somewhat understand. Ihave always had a difficult time solving story problems. Reall I donot know where to begin.

A conical tank (inverted right circular cone) filledwith water is 10 ft. across the top and 12 ft. high. How much workis needed to pump all the water out over the top.

How much work is needed inExercise 15 to pump 4 ft. of water out over the top (a) when thetank is full? (b) when the tank has 4 ft. of water in it?

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## Answers ( 1 )

first try to draw a picture of the problem:

where

now remember the integral related to work:

where x in this case represents the distance the water has to belifted, and the function represents the area of the water beinglifted at height h times the :

Since we are talking about a cone, the area of water that has to belifted at height h is:

We need this area function in terms of h, to get this we usesimilar triangles:

(since w represents the radius of the cone, it is one half thewidth of the cone)

so we have our integral:

(12-h because the work increases the smaller h is)

evaluate the integral to get the answer.

How muchwork is needed in Exercise 15 to pump 4 ft. of water out over thetop (a) when the tank is full? (b) when the tank has 4 ft. of waterin it?

a) evaluate the integral from 8 to 12 (the top 4 ftof the tank)

b)evaluate the integral from 0 to 4 (the bottom 4ft of thetank)