   Chapter 9.3, Problem 37E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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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