Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram illustrates a solid cone with slant height of $15\text{ cm}$ and vertical height $h\text{ cm}$.
(i)[2]

Show that the cone’s volume, $V\text{ cm}^3$, can be written as $V = \frac{1}{3}\pi(225h - h^3)$. [For a cone with radius $r$ and vertical height $h$, the volume is $\frac{1}{3}\pi r^2 h$.]

(ii)[5]

Given that $h$ may change, determine the value of $h$ for which $V$ is stationary. Show all required working and state the nature of this stationary value.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies Pythagoras’ theorem to give $y^2=15^2-h^2$

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