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Sand is pouring at the rate of 12 cm^(3)...

Sand is pouring at the rate of `12 cm^(3)"/sec"`. The falling sand forms a cone on the ground in such a way that the height of the cone is always `((1)/(6))^(th)` of the radius of the base. If the height of sand is 4 cm, then the rate at which height of sand increasing, is

A

`(1)/(12 pi)` cm/sec

B

`(1)/(6pi)` cm/sec

C

`(1)/(48 pi)` cm/sec

D

`(1)/(24 pi)` cm/sec

Text Solution

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The correct Answer is:
C
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