Question

If the water is being poured at the rate 36 m ³/s in a cylindrical vessel of base radius 3 m, then the rate at which water level is rising, is ______.

Options

• `3/π` m/s

• `π/4` m/s

• `4/π` m/s

• 4π m/s

Answer 1

If the water is being poured at the rate 36 m ³/s in a cylindrical vessel of base radius 3 m, then the rate at which water level is rising, is `underlinebb(4/π m//s)`.

Explanation:

Let V, r, h be the volume, radius and height of a cylindrical vessel respectively.

∴ `(dV)/dt` = 36 m³/s

Now, V = πr²h    ...(i)

On differentiating equation (i) w.r.t. ‘t’, we get

`(dV)/dt = πr^2 (dh)/dt`

`\implies (dh)/dt = (((dV)/dt))/(πr^2) = 36/(π(3)^2)`  ...[∵ r = 3]

`\implies (dh)/dt = 4/π` m/s

Hence, the water level is rising at the rate of `4/π` m/s.