Chapter 2.7, Problem 15E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A spherical balloon is being inflated. Find the rate of increase of the surface area
*r* when *r* is (a) 1 ft, (b) 2 ft, and (c) 3 ft. What conclusion can you make?

To determine

**To find**: The rate of increase of the surface area with respect to the radius r when r is

(a) 1 ft, (b) 2 ft, and (c) 3 ft then make conclusion.

Explanation

**Conclusion**:

We can conclude that, the rate of increase of surface area of balloon is linear with respect to the radius..

**1) Concept:**

Use concept of derivative to find the rate of increase of the surface area with respect to the radius r.

**2) Formula:**

i. Surface area of a spherical balloonÂ

ii. Power rule of derivative:

**3) Given**:

(a) r = 1 ft, (b) r = 2 ft, and (c) r = 3 ft

**4) Calculation:**

Surface area of a spherical balloon

Now, find derivative of

By using power rule of derivative,

**(a)** To find the rate of increase of the surface area at r = 1, substitute r = 1 in

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