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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
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Related RatesRight circular cylinder The total surface

Chapter 3, Problem 141PE

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QUESTION:

Problem 141PE

Related Rates

Right circular cylinder The total surface area S of a right circular cylinder is related to the base radius r and height h by the equation

a. How is dS/dt related to dr/dt if h is constant?

b. How is dS/dt related to dr/dt if r is constant?

c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant?

d. How is dS/dt related to dr/dt if S is constant?

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QUESTION:

Problem 141PE

Related Rates

Right circular cylinder The total surface area S of a right circular cylinder is related to the base radius r and height h by the equation

a. How is dS/dt related to dr/dt if h is constant?

b. How is dS/dt related to dr/dt if r is constant?

c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant?

d. How is dS/dt related to dr/dt if S is constant?

ANSWER:

Solution:

Step 1 of 2:

In this problem, we need to explain the following given conditions.

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