   Chapter 9.3, Problem 37E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# For a right circular cone, the ratio of the slant height to the length of the radius is 5 : 3. If the volume of the cone is 96 π  in 3 , find the lateral area of the cone.

To determine

To find:

The lateral area of the cone.

Explanation

Given:

For a right circular cone, the ratio of the slant height to the radius is 5:3. If the volume of the cone is 96π in3.

Formula used:

The volume of the right circular cone is V=13πr2h.

The Lateral area of the cone is L=πrl.

Calculation:

Let l be the slant height of the cone and r be the radius.

The ratio of the slant height to the radius is 5:3.

Let us assume l=5t,r=3t.

In a right circular cone r2+h2=l2.

r2+h2=l2(3t)2+h2=(5t)29t2+h2=25t2h2=25t29t2h2=16t2h=16t2h=4t

The volume of the cone is 96π in3.

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