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Leto [7]
3 years ago
15

PLEASE SHOW WORK

Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0

(C)

Step-by-step explanation:

The volume of the conical pile is given by

V = \dfrac{\pi}{3}r^2h

Taking the derivative of V with respect to time, we get

\dfrac{dV}{dt} = \dfrac{\pi}{3}\dfrac{d}{dt}(r^2h)

\:\:\:\:\:\:\:= \dfrac{\pi}{3}\left(2rh\dfrac{dr}{dt} + r^2\dfrac{dh}{dt}\right)

Since r is always equal to h, we can set

\dfrac{dr}{dt} = \dfrac{dh}{dt}

so that our expression for dV/dt becomes

\dfrac{dV}{dt} = \dfrac{\pi}{3}\left(3r^2\dfrac{dh}{dt}\right)

\:\:\:\:\:\:\:= \pi r^2\dfrac{dh}{dt}

Solving for dh/dt, we get

\dfrac{dh}{dt} = \dfrac{1}{\pi r^2}\dfrac{dV}{dt}

\:\:\:\:\:\:\:= \dfrac{1}{9\pi\:\text{m}^2}(36\:\text{m}^3\text{/s})

\:\:\:\:\:\:\:= \dfrac{4}{\pi}\:\text{m/s}

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