A solid cylinder of height has a conical portion of the same height and radius…

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

Problem

A solid cylinder of height

h

has a conical portion of the same height and radius

\frac{h}{3}

removed from it. Rainwater accumulates in it at a rate equal to

\pi

times the instantaneous radius of the water surface inside the hole. The time after which the hole will be filled with water is (1)

\frac{h^2}{3}

(2)

h^2

(3)

\frac{h^2}{6}

(4)

\frac{h^2}{4}