Chapter 9.4, Problem 30E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

A sphere is inscribed in a right circular cone whose slant height has a length equal to that of the diameter of its base. What is the length of the radius of the sphere if the slant height and the diameter of the cone both measure 12 cm?

To determine

**To find:**

The length of the radius of the sphere, inscribed in a right circular cone.

Explanation

**Approach:**

A sphere is a three dimensional solid figure, which is made up of all the points in space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere.

The surface area of a sphere *S* *r* is the radius of the sphere.

Volume of a sphere *V* =

For right circular cone of base radius (*r*), slant height (*l*) and altitude (*h*),

Total surface area of the cone =

Curved or lateral surface area of the cone =

Volume of the cone =

The Pythagorean theorem for a right angle triangle states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The longest side of the right angle triangle is called the hypotenuse.

**Calculation:**

Consider a sphere inscribed in a right circular cone. The slant height of the cone has length equal to the diameter of its base.

For right circular cone of base radius (*r*), slant height (*l*) and altitude (*h*), and radius of sphere = (R).

slant height of cone = 12 cm = (*l)*

diameter of the cone = 12 cm = (*d*)

radius of cone = (r) = 6 cm

By using Pythagorean Theorem,

In the above figure

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