Question

Water is being poured at the rate of 27 m³/sec into a cylindrical vessel of base radius 3 m. Find the rate at which the water level is rising.

Answer 1

Let r be the radius of the base, h be the height and V be the volume of the cylindrical vessel at time t.

Given: `(dV)/(dt) = 27` m³/sec and r = 3 m.

Now, V = πr²h

= π(3)²h

= 9πh

Differentiating w.r.t. t, we get

`(dV)/(dt) = 9π (dh)/(dt)`

∴ `(dh)/(dt) = 1/(9π) * (dV)/(dt)`

= `1/(9π) xx 27`

= `3/π`

Hence, the water level is rising at the rate of `(3/π)` m/sec.