AM-2116

Connected rates of change

A Math · Secondary 4 · Hard · Connected rates of change

Water is poured at a constant rate of

6\text{ cm}^3\text{/s}

into an inverted right cone. The height of the cone is three times its radius. The volume

V

of water of height

h

in the cone is given by

V=\tfrac13\pi r^2h

.

Find

\dfrac{dh}{dt}

when the water level is

9\text{ cm}

high.

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