Question

A cylindrical tank of radius 10 cm is being filled with sugar at the rate of 100π cm³/s. The rate, at which the height of the sugar inside the tank is increasing, is ______.

Options

• 0.1 cm/s

• 0.5 cm/s

• 1 cm/s

• 1.1 cm/s

Answer 1

A cylindrical tank of radius 10 cm is being filled with sugar at the rate of 100π cm³/s. The rate, at which the height of the sugar inside the tank is increasing, is 1 cm/s.

Explanation:

Given: r = 10 cm

`(dv)/(dt) = 100 pi  cm^3//sec`

Volume of cylinder,

v = πr²h

= 100 πh

Differentiating on both sides,

`(dv)/(dt) = 100 pi  (dh)/(dt)`

`100 pi = 100 pi  (dh)/(dt)`

`(dh)/(dt) = 1  cm//sec`