Chapter 5.R, Problem 29E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis.

(a) If its height is 4 ft and the radius at the top is 4 ft, find the work required to pump the water out of the tank.

(b) After 4000 ftâ€“lb of work has been done, what is the depth of the water remaining in the tank?

To determine

**(a)**

**To find:**

The work required to pump the water out of the tank.

Explanation

**1) Concept:**

The work is calculated by using the formula

**2) Given:**

The height of the paraboloid is

The radius of the paraboloid is

**3) Calculations:**

The vertex of the parabola is at origin and passing through point

Therefore, the equation of the parabola is

Substitute values of

Solving for

Hence,

That is,

Therefore,

Each circular disk has radius

And water weighs

Therefore, the work required to pump the water out of the tank is

To determine

(b)

**To find:**

The depth of water remaining in the tank after

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