Question Detail

MTH 102 Differentiation Objective Question
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Question

A cylinder's radius increases at 2 cm/sec, height decreases at 3 cm/sec. Rate of change of volume when both are 10 cm?
Options
A \( 100\pi \text{ cm}^3/\text{sec} \)
Correct Answer
B \( 400\pi \text{ cm}^3/\text{sec} \)
C \( -300\pi \text{ cm}^3/\text{sec} \)
D \( 100 \text{ cm}^3/\text{sec} \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

( V = \pi r^2 h \implies \dot{V} = \pi(2rh\dot{r} + r^2\dot{h}) ). Given ( r=10, h=10, \dot{r}=2, \dot{h}=-3 ). ( \dot{V} = \pi(2(10)(10)(2) + 100(-3)) = \pi(400 - 300) = 100\pi ).

Hint

Differentiate the volume formula using the product rule.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 155 of 930
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