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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 11.CR, Problem 34CR
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Elementary Geometry for College St...

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

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Problem 34CR
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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 m∠A=θ we have the following ratios.

sin⁡θ=OppositeHypotenuse

cos⁡θ=AdjacentHypotenuse

tan⁡θ=OppositeAdjacent

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

m∠OAC=65°

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

Thus,

CA=r=3.2ft=Adjacent

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Sect-11.1 P-1ESect-11.1 P-2ESect-11.1 P-3ESect-11.1 P-4ESect-11.1 P-5ESect-11.1 P-6ESect-11.1 P-7ESect-11.1 P-8ESect-11.1 P-9ESect-11.1 P-10E
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