Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

A hemisphere with radius $r$ cm is attached to a cone of radius $r$ cm and height $h$ cm to make the solid. The hemisphere's volume is one third of the volume of the whole solid.
(a)[2]

Find $h$ in terms of $r$.

(b)[2]

The cone's slant height can be written as $r\sqrt{k}$ cm, where $k$ is an integer. Find the value of $k$.

(c)[1]

Find an expression, in terms of $r$ and $\pi$, for the total surface area, in $\text{cm}^2$, of the solid.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: $h=4r$

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