Edexcel IGCSE Math A 4.10.E The volume of prisms

Practise finding volumes of cuboids, cylinders and prisms, including missing lengths, water contexts and compound diagrams.

Exam points

set up volume equations for cuboids or cylinders to find a missing height or width
use cross-sectional area × length for prisms, including triangular sections
compare container volumes in water or packing problems before finding remaining space

[Maximum number: 3]

The diagram shows a cuboid and a cylinder.

Figure for Question 4.10.E The volume of prisms question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

The dimensions of the cuboid are $x \mathrm{~cm}$ by 12 cm by 5 cm .
The volume of the cuboid is $270 \mathrm{~cm}^{3}$
The radius of the cylinder is $x \mathrm{~cm}$ .
The height of the cylinder is $2 x \mathrm{~cm}$ .

Work out the volume of the cylinder.

Give your answer correct to the nearest whole number.

Radius:
$r=\frac{270}{12\times5}=4.5$

Volume:
$\pi r^{2}h=\pi\times4.5^{2}\times9 = 572.5\ldots$

Final answer:
573

A1 accepts 572 to 573.

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4.10.E The volume of prisms question 1