Mathematics 0580 · IGCSE · Pythagoras' theorem and trigonometry in 3D

Pythagoras' theorem and trigonometry in 3D — practice question

(a)[3]

The sketch depicts a hemisphere with radius $6\text{ cm}$. Work out its volume. Include the units in your answer. [For a sphere of radius $r$, the volume is $V = \frac{4}{3}\pi r^3$.]

(b(i))[6]

The diagram is of prism $ABCDEF$. Its cross-section is the right-angled triangle $BCD$. Here $BD = 10\text{ cm}$, $BC = 5.2\text{ cm}$ and $ED = 18\text{ cm}$. Find the volume of the prism.

(b(ii))[4]

Calculate angle $BEC$.

(b(iii))[3]

Point $G$ is on the line $ED$, with $GD = 7\text{ cm}$. Find angle $BGE$.

Worked solution & mark scheme

This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: Approximately $452 \text{ cm}^3$ (accept $452.2$ to $452.4$)

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