Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram depicts a water container shaped like an inverted pyramid, arranged so that when the water depth is $h$ cm, the water surface is a square with side $\frac{1}{2}h$ cm.
(i)[1]

Write the volume of water in the container as a formula in $h$. [For a pyramid with base area $A$ and perpendicular height $h$, the volume is $\frac{1}{3}Ah$.]

(ii)[4]

Water enters the container by dripping at a steady rate of $20\text{ cm}^3$ per minute. Determine the speed, in cm per minute, at which the water level is rising when the water depth is $10$ cm.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Therefore, use $V=\frac{1}{12}h^3$

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