An inverted right circular conical tank has a height of 15 m and a base radius of 6 m

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

An inverted right circular conical tank has a height of 15 m and a base radius of 6 m. Water is pumped into the tank at 4 m

^{3}

/min, but water also leaks through a hole at a rate of

0.1h

^{3}

/min, where

h

(in meters) is the current water depth. At the moment when

h=9

m, what is the rate of change of the water’s surface radius

r

? (a)

-\dfrac{25}{162\pi}\text{ m/min}

(b)

\dfrac{31}{324\pi}\text{ m/min}

(c)

\dfrac{10}{81\pi}\text{ m/min}

(d)

\dfrac{31}{972\pi}\text{ m/min}