   Chapter 9.CR, Problem 15CR 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

The slant height of a right circular cone is 12 cm. The angle formed by the slant height and altitude is 30⁰. Find the exact and approximate a) Lateral area b) total area c) volume.

To determine

(a)

To find:

The lateral area of the right circular cone.

Explanation

Formula used:

Lateral area L of any prism whose altitude has measure h and whose base has radius r is given by the formula,

L=πrl

Given:

The slant height of a right circular cone is 12 cm. The angle formed by the slant height and altitude is 30⁰.

Calculation:

Let L=πrl                              (1)

Right circular cone as shown in the above figure.

The angle formed by the slant height and altitude is 30⁰.

Then the height of the right circular cone is,

h=12sin30=1232h=63cm

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

To determine

(b)

To find:

The total area of the right circular cone.

To determine

(c)

To find:

The volume of the right circular cone.

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