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Question

A spherical iron ball of radius 10cm, coated with a layer of ice of uniform thickness, melts at a rate of 100πcubiccm/min. The rate at which the thickness layer decreases, when the thickness of ice is 5cm, is


A

1cm/min

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B

2cm/min

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C

1376cm/min

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D

5cm/min

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E

3cm/min

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Solution

The correct option is A

1cm/min


Explanation for the correct option:

Step 1. Put the value of V in dVdt:

dVdt=100πcm3/min

ddt43πr3=100π

3r2drdt=300π4π

Step 2. Put the value of r=5:

drdt=3004×3×25

=1cm/min

The rate of decrease of thickness is 1cm/min

Hence, Option ‘A’ is Correct.


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