The height of a tank in the form of an inverted cone is and the radius of its…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The height of a tank in the form of an inverted cone is

10\,\mathrm{m}

and the radius of its circular base is

2\,\mathrm{m}

. The tank contains water and leaks through a hole at its vertex at a rate of

0.02\,\mathrm{m^3\,s^{-1}}

. Find the rate at which the water level changes and the rate at which the radius of the water surface changes when the water height is

5\,\mathrm{m}