(a)
To find: The rate of increase the surface area of the balloon of radius 1 ft.
(a)
Answer to Problem 15E
The rate of increase of surface area of the balloon of radius 1 ft is,
Explanation of Solution
Surface area of the balloon is,
The rate of change of the balloon with respect to its radius is,
The rate of increase of surface area of radius 1 ft is,
The rate of increase of the surface area of the balloon of radius 1 ft is,
(b)
To find: The rate of increase the surface area of the balloon of radius 2 ft.
(b)
Answer to Problem 15E
The rate of increase of surface area of the balloon of radius 2 ft is,
Explanation of Solution
Surface area of the balloon is,
The rate of change of the balloon with respect to its radius is,
The rate of increase of surface area of radius 2 ft is,
Therefore, the rate of increase of the surface area of the balloon of radius 2 ft is,
(c)
To find: The rate of increase the surface area of the balloon of radius 3 ft. What can be concluded from the parts (a), (b) and (c)?
(c)
Answer to Problem 15E
The rate of increase of surface area of the balloon of radius 3 ft is,
Explanation of Solution
Surface area of the balloon is,
The rate of change of the balloon with respect to its radius is,
The rate of increase of surface area of radius 3 ft is,
The rate of increase of the surface area of the balloon of radius 3 ft is,
Thus, the value of the rate of increase of surface area increases as the radius increases.
From the parts (a), (b) and (c), it can be concluded that the rate of change increases as radius increases.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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