   Chapter 15.8, Problem 16E

Chapter
Section
Textbook Problem

(a) Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have positioned the coordinate system that you have chosen.(b) Suppose the ball is cut in half. Write inequalities that describes one of the halves.

(a)

To determine

To write: The inequalities that describe the given hollow ball.

Explanation

Given:

The diameter of the hollow ball is 30 cm and the thickness is 0.5 cm.

Since the ball is of diameter 30 cm, the radius of the ball is 15 cm.

So, ρ varies from 14.5 to 15. Since it is the ball, θ varies from 0 to 2π .

For ϕ , the limit varies from 0 to π because for the ball it is calculated only from the north pole to south pole. Thus, for 2π , the area will be counted as twice

(b)

To determine

To write: The inequalities that describe the given hollow ball which cut into half.

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