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Cambridge IGCSE Maths: Mensuration — Practice Questions & Answers
Mensuration is the branch of mathematics that measures geometric shapes: their perimeters, areas, surface areas and volumes. This guide covers every standard 2D and 3D shape in the IGCSE 0580 syllabus, from rectangles and circles to cones, spheres and pyramids, plus circle parts (arcs and sectors), compound figures, and the all-important rules for converting between units of length, area and volume.
258 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
A rectangle has length $8$ cm and width $5$ cm. What is its area?
$40$ cm$^{2}$
$26$ cm$^{2}$
$20$ cm$^{2}$
$13$ cm$^{2}$
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Why Area of a rectangle $=$ length $\times$ width $= 8 \times 5 = 40$ cm$^{2}$.
2
Multiple choice · Easy
A rectangle has length $12$ m and width $7$ m. What is its perimeter?
$38$ m
$84$ m
$19$ m
$24$ m
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Why Perimeter $= 2(\text{length} + \text{width}) = 2(12 + 7) = 38$ m.
3
Multiple choice · Easy
A triangle has base $10$ cm and perpendicular height $6$ cm. What is its area?
$30$ cm$^{2}$
$60$ cm$^{2}$
$16$ cm$^{2}$
$8$ cm$^{2}$
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Why Area of a triangle $= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 6 = 30$ cm$^{2}$.
4
Multiple choice · Easy
A circle has radius $7$ cm. Taking $\pi = 3.142$, what is its area to $2$ decimal places?
$153.94$ cm$^{2}$
$43.98$ cm$^{2}$
$21.99$ cm$^{2}$
$615.75$ cm$^{2}$
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Why Area $= \pi r^{2} = \pi \times 7^{2} = \pi \times 49 = 153.94$ cm$^{2}$.
5
Multiple choice · Easy
A circle has radius $5$ cm. What is its circumference to $2$ decimal places?
$31.42$ cm
$78.54$ cm
$15.71$ cm
$10$ cm
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Why Circumference $= 2 \pi r = 2 \times \pi \times 5 = 31.42$ cm.
6
Multiple choice · Easy
A parallelogram has base $9$ cm and perpendicular height $4$ cm. What is its area?
$36$ cm$^{2}$
$18$ cm$^{2}$
$13$ cm$^{2}$
$26$ cm$^{2}$
Tap an answer to check it.
Why Area of a parallelogram $= \text{base} \times \text{height} = 9 \times 4 = 36$ cm$^{2}$.
7
Multiple choice · Easy
A trapezium has parallel sides of $6$ cm and $10$ cm, with a perpendicular distance of $4$ cm between them. What is its area?
$32$ cm$^{2}$
$64$ cm$^{2}$
$80$ cm$^{2}$
$20$ cm$^{2}$
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Why Area of a trapezium $= \frac{1}{2}(a + b) \times h = \frac{1}{2}(6 + 10) \times 4 = 32$ cm$^{2}$.
8
Multiple choice · Easy
A cuboid measures $5$ cm by $4$ cm by $3$ cm. What is its volume?
$60$ cm$^{3}$
$94$ cm$^{3}$
$12$ cm$^{3}$
$47$ cm$^{3}$
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Why Volume of a cuboid $= \text{length} \times \text{width} \times \text{height} = 5 \times 4 \times 3 = 60$ cm$^{3}$.
9
Multiple choice · Easy
How many centimetres are there in $3$ metres?
$300$ cm
$30$ cm
$3000$ cm
$0.03$ cm
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Why There are $100$ cm in $1$ m, so $3 \times 100 = 300$ cm.
10
Multiple choice · Medium
A cylinder has radius $3$ cm and height $10$ cm. What is its volume to $2$ decimal places?
$282.74$ cm$^{3}$
$94.25$ cm$^{3}$
$188.50$ cm$^{3}$
$28.27$ cm$^{3}$
Tap an answer to check it.
Why Volume of a cylinder $= \pi r^{2} h = \pi \times 3^{2} \times 10 = \pi \times 90 = 282.74$ cm$^{3}$.
Key terms in Mensuration
Perimeter: The total distance around the edge of a two-dimensional shape.
Area: The amount of surface a two-dimensional shape covers, measured in square units.
Area of a rectangle: The product of length and width, $A = lw$.
Area of a triangle: Half the base times the height, $A = \frac{1}{2}bh$.
Area of a parallelogram: The base times the perpendicular height, $A = bh$.
Area of a trapezium: Half the sum of the parallel sides times the height, $A = \frac{1}{2}(a+b)h$.
Circumference: The perimeter of a circle, found from $C = 2\pi r$ or $C = \pi d$.
Area of a circle: The space inside a circle, given by $A = \pi r^2$.
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