   Chapter 11.CR, Problem 34CR 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

In a right circular cone, the radius of the base is 3.2 ft in length and the angle formed by the radius and slant height measures θ = 65 ° . To the nearest tenth of a foot, find the length of the altitude of the cone. Then use this length of altitude to find the volume of the cone to the nearest tenth of a cubic foot.

To determine

To find:

Find the volume of the cone to the nearest tenth of a cubic foot.

Explanation

Procedure used:

In any right triangle ABC with mA=θ we have the following ratios.

sinθ=OppositeHypotenuse

Calculation:

Given:

Radius of aright circular cone =3.2 ft. Angle between the radius and the slant height =65°.

Let the cone be represented by OABC as shown in the following figure.

In the above cone we have the radius r = 3.2 ft and let ‘h’ be the altitude of the cone.

Thus,

r = 3.2 ft and

OC=h

mOAC=65°

Consider the triangle OAC of the cone which is a right triangle having right angle at ‘c’.

Thus,

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