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Question: Sand is pouring from a pipe at the rate of 12cm<sup>3</sup>/sec. The falling sand forms a cone on th...

Sand is pouring from a pipe at the rate of 12cm3/sec. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand-cone increasing when the height is 4cm –

A

48 p cm/sec

B

148π\frac { 1 } { 48 \pi } cm/sec

C

58 p cm/sec

D

) 158π\frac { 1 } { 58 \pi } cm/sec

Answer

148π\frac { 1 } { 48 \pi } cm/sec

Explanation

Solution

At time t

V = 13\frac { 1 } { 3 }p . (36 h2) . h

Pipe

We required dhdt\frac { \mathrm { dh } } { \mathrm { dt } }