Water is dripping out from a conical funnel of semi-vertical angle at the uniform…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Water is dripping out from a conical funnel of semi-vertical angle

\frac{\pi}{4}

at the uniform rate of

2\,\text{cm}^3/\text{sec}

in its surface area through a tiny hole at the vertex in the bottom. When the slant height of the water is

4\,\text{cm}

, then the rate of decrease of the slant height of the water, is - (a)

\frac{\sqrt{6}}{4\pi}\,\text{cm/sec}

(b)

\frac{\sqrt{5}}{4\pi}\,\text{cm/sec}

(c)

\frac{\sqrt{2}}{4\pi}\,\text{cm/sec}

(d)

\frac{\sqrt{3}}{4\pi}\,\text{cm/sec}