About Mensuration in O Level Mathematics
Mensuration is one of the 5 main topics in our O Level Mathematics (Cambridge (CAIE) 4024) question bank, and about 6% of its real questions come from it. Tayyari Karo has 22 real questions on this topic from 2021 to 2026, from Paper 1, Paper 2. By difficulty: 10 hard, 8 medium, 4 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
May/June 2025 · Paper 1 · Mensuration
OAB is a minor sector of a circle, centre O. OCD is a major sector of a different circle, also centre O. OCA and ODB are straight lines (so C lies on OA and D lies on OB). OC = 6 cm and OA = 9 cm. The length of the minor arc AB is 5π cm.
Work out the area of the major sector OCD. Give your answer in terms of π.
Show model answer
Arc length = rθ (θ in radians), using radius OA = 9:
5π = 9θ
θ = 5π/9 radians = 100°
Since OCA and ODB are straight lines, angle COD = angle AOB = 100°.
Major sector OCD has angle 360 − 100 = 260°.
Area of major sector = (260/360) × π × OC²
= (13/18) × π × 6²
= (13/18) × 36π
= 26π
Area of major sector OCD = 26π cm²
Use arc length = rθ to find the sector angle, then the major sector uses the reflex angle 360° − θ.
Oct/Nov 2025 · Paper 1 · Mensuration
A circle has diameter 12 cm.
Find the area of the circle. Give your answer in terms of π.
Show model answer
Radius = 12 ÷ 2 = 6 cm
Area = πr² = π × 6²
= 36π cm²
Halve the diameter to get the radius, then use A = πr².
Oct/Nov 2025 · Paper 2 · Mensuration
The net of a cuboid has three different edge lengths: 3 cm, 5.2 cm and 4.7 cm (all lengths in centimetres).
(a) Find the total surface area of the cuboid.
(b) Write down the number of planes of symmetry of the cuboid.
Show model answer
(a) Surface area = 2(lw + lh + wh), with l = 3, w = 5.2, h = 4.7
= 2(3×5.2 + 3×4.7 + 5.2×4.7)
= 2(15.6 + 14.1 + 24.44)
= 2(54.14)
= 108.28
≈ 108 cm² (3 s.f.)
(b) A cuboid with three different edge lengths has 3 planes of symmetry (one parallel to each pair of opposite faces).
Add the areas of the three pairs of faces and double; a general cuboid has one plane of symmetry parallel to each pair of faces.
May/June 2024 · Paper 1 · Mensuration
Prism A and prism B are mathematically similar. The volume of prism A is 5000 cm³. The length of prism A is 50 cm. The area of the cross-section of prism B is 16 cm².
Calculate the length of prism B.
Show model answer
Cross-sectional area of prism A = Volume ÷ length = 5000 ÷ 50 = 100 cm²
Area scale factor (B to A) = 16/100 = 0.16
Length scale factor = √0.16 = 0.4
Length of prism B = 50 × 0.4 = 20 cm
Find the cross-sectional area of A first; the length scale factor is the square root of the area scale factor.
Oct/Nov 2024 · Paper 1 · Mensuration
A sector of a circle with angle 60° has arc length 4π cm.
Find the area of the sector. Give your answer, as simply as possible, in terms of π.
Show model answer
Arc length = (θ/360) × 2πr
4π = (60/360) × 2πr
4π = (1/6) × 2πr
4π = πr/3
r/3 = 4
r = 12
Area of sector = (θ/360) × πr²
= (60/360) × π × 12²
= (1/6) × 144π
= 24π
Area = 24π cm²
Use the arc-length formula to find the radius first, then substitute into the sector-area formula.
May/June 2023 · Paper 1 · Mensuration
OMN is a sector of a circle, centre O. ON = 20 cm and the angle of the sector is x°. The area of the sector is 30π cm².
Find the value of x.
Show model answer
Area of sector = (x/360) × πr²
r = 20, so r² = 400
30π = (x/360) × π × 400
30 = (x/360) × 400
x = 30 × 360 / 400
x = 27
Use the sector-area formula and cancel π from both sides before solving for x.
May/June 2022 · Paper 1 · Mensuration
Two cubes have a total volume of 152 cm³. One cube has an edge of length 5 cm.
(a) Calculate the length of the edge of the other cube.
(b) Work out the total length of all of the edges of the larger cube.
Show model answer
(a) Volume of first cube = 5³ = 125 cm³
Volume of other cube = 152 − 125 = 27 cm³
Edge = ∛27 = 3 cm
(b) The larger cube has edge 5 cm and a cube has 12 edges.
Total edge length = 12 × 5 = 60 cm
Subtract to find the missing volume, take a cube root for the edge, then multiply by 12 edges.
May/June 2021 · Paper 1 · Mensuration
Trapezium ABCD has parallel sides AB = 7 cm and DC = 10 cm. The area of ABCD is 85 cm². The perpendicular height of the trapezium is h cm.
Find the value of h.
Show model answer
Area of trapezium = (1/2)(a + b)h
85 = (1/2)(7 + 10)h
85 = 8.5h
h = 85 ÷ 8.5
h = 10
Use the trapezium area formula and solve for the height.
