Sand is falling into a conical pile at the rate of 10 m^3/s such that height of the pile is always half the diameter of the base of the pile find the rate at which the height of the pile is changing when the pile is 5 m. high.

The rate at which the height of the pile is .

Explanation:

Given that,

Height = radius = 5 m

Rate = 10 m³/s

We need to calculate the rate at which the height of the pile

Using formula of volume

r = h,

On differentiating

Put the value into the formula

Hence, The rate at which the height of the pile is .

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