Chapter 15.9, Problem 21E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Evaluate ∫∫∫* _{E} dV*, where

(b) The earth is not a perfect sphere; rotation has resulted in flattening at the poles. So the shape can be approximated by an ellipsoid with *a* = *b =* 6378 km and *c* = 6356 km. Use part (a) to estimate the volume of the earth.

(c) If the solid of part (a) has constant density *k*. find its moment of inertia about the z-axis.

(a)

To determine

**To evaluate:** The integral

Explanation

**Given:**

The region *E* is enclose by the ellipsoid

**Formula used:**

The Jacobian value *J* is,

**Calculation:**

Find the partial derivative of *x*, *y* and *z* with respect to *u*, *v* and *w*, respectively*.*

If

If

If

Obtain the Jacobian value *J*.

(b)

To determine

**To estimate:** The volume of the earth.

(c)

To determine

**To find:** The moment of inertia of the solid from part (a) is,
*z*-axis with constant density *k*.

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