5. The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. What is the rate of change of the volume of the cylinder, in cm3/min, when the radius is 2 cm and the height is 3 cm? (Note: The volume of a right circular cylinder is V =
p r2h.)
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A. -2p |
B. -8 p /5 |
C. -3 p /5 |
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D. 2 p /5 |
E. 2 p |
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Solution: The answer is D
Given,
Differentiating both sides results in the following differential equation,
Since,
By substitution,
Thus, when r = 2 and h = 3,
