Water is poured into a right circular cone at the constant rate of

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

2\,\text{cm}^{3}\!\!\text{/s}

. The cone has a fixed height of

12\,\text{cm}

and a semi-vertical angle of

30^{\circ}

. Let

h\,(\text{cm})

be the depth of water at time

t\,(\text{s})

. (i) Establish a relation between the volume of water

V

and the depth

h

. (ii) Determine the rate at which the water level is rising when

h = 8\,\text{cm}