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Question

The radius of a cylinder is increasing at the rate of 5cm/min, so that its volume is constant. When its radius is 5cmand height is 3cm, then the rate of decreasing of its height is


A

6cm/min

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B

3cm/min

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C

5cm/min

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D

2cm/min

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Solution

The correct option is A

6cm/min


Explanation for the correct answer

Given,

drdt=5cmmin

dVdt=0

We need to find the rate of decrease in heightdhdt

We know that volume of the cylinder is

V=πr2h

On differentiating the volume concerning the radius

dVdt=πr2dhdt+2πrhdrdt

At r=5mand h=3m,

0=2πrhdrdt+πr2dhdtπr2dhdt=2πrhdrdtπ(5)2dhdt=2π×5×5×3dhdt=-6cmmin

As we need a decreasing rate of its heightdhdt=6cmmin, a negative sign implies decreasing.

Hence the rate of decreasing height of the cylinder is 6cmmin


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