Sand is being poured to form a conical pile whose base rests on a horizontal surface

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Sand is being poured to form a conical pile whose base rests on a horizontal surface. The sand is added at a constant rate of 0.4 m

^{3}

/min. The angle of repose of the sand (the constant angle between the side of the cone and the horizontal) is 35°. (a) Express the radius

r

of the base of the sand pile as a function of its height

h

. (b) Derive a formula for

\dfrac{dh}{dt}

in terms of

h

. (c) Compute

\dfrac{dh}{dt}

when the pile is 2 m high, interpreting your result in context.