Chapter 9.CR, Problem 19CR

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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The solid shown consists of a hemisphere (half of a sphere), a cylinder, and a cone. Find the exact volume of the solid.

To determine

**To find:**

The exact volume of the solid.

Explanation

**Formula used:**

Volume of half sphere:

Volume of cylinder:

Volume of cone:

**Given:**

The solid shown consists of a hemisphere (half of a sphere) a cylinder and a cone.

**Calculation:**

The volume of given solid is,

First we find the height of the cone,

Right circular cone as shown in the above figure.

Also, the slant height is the hypotenuse of a right circular cone with legs equal to the lengths of the altitude of the cone and the radius of the base.

Applying the Pythagorean Theorem,

The height of the cone is

Next we find the height of the cylinder,

Already we know that, in the given solid the radius of cone is same as to the radius of half sphere.

Also, the radius of half sphere is same as to the height of the half sphere.

So, the height of the half sphere is

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