An inverted right circular cone has a height of m and a base radius of m

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

An inverted right circular cone has a height of

8\,

m and a base radius of

4\,

m. Water is pumped into the cone at

7\,

^{3}

/min, but a leak lets water escape at a rate of

0.4h\,

^{3}

/min, where

h

(in m) is the instantaneous water depth. Find

\dfrac{dh}{dt}

when

h=5\,

m. Express your answer in exact form (m/min).