Chapter 9.4, Problem 46E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Suppose that a semicircular region with vertical diameter of length 4 is rotated about that diameter. Determine the exact surface area and the exact volume of the resulting solid of revolution.

To determine

**To find:**

The surface area and volume of the solid of revolution.

Explanation

**Approach:**

A solid of revolution is obtained by rotating a plane region around a straight line lying on the same plane. The straight line is called the axis of revolution. It may be vertical, horizontal or oblique.

A sphere is a three dimensional solid figure, which is made up of all the points in space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere. The surface area of a sphere *S* = *r *is the radius of the sphere.

All solid bodies occupy space. The measure of occupied space is called the volume of the object. Volume of a sphere = *V *=

**Calculation:**

Consider a semi circular region that is rotated about its vertical diameter. The resultant solid of revolution that is formed is a sphere, with diameter *d *= 4.

Radius *r *=

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