Mensuration: past paper questions

Real questions on mensuration

The newest 20 of 126 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q11[3]

   3-mark question — its maths and diagrams are best seen on the paper.

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2. 0580/12 · May/June 2026 · Q11a[1]
   11 Complete these statements. (a) 2 kg is the same as ................................ g.See it on the paper →
3. 0580/12 · May/June 2026 · Q11b[1]
   11 Complete these statements. (b) $7{\text{ cm}}^2$ is the same as ........................ ${\text{mm}}^2$.See it on the paper →
4. 0580/12 · May/June 2026 · Q12a[1]
   12 To make a solid, a net is drawn on the $1{\text{cm}}^2$ grid. [Diagram: A net of a cuboid drawn on a grid, consisting of six rectangles. The net has a central horizontal row of four rectangles, with one rectangle attached above the second rectangle from the left, and one rectangle attached below the third rectangle f...See it on the paper →
5. 0580/12 · May/June 2026 · Q12b[2]

   2-mark question — its maths and diagrams are best seen on the paper.

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6. 0580/13 · May/June 2026 · Q14b[2]
   (b) Find the volume of the triangular prism.See it on the paper →
7. 0580/13 · May/June 2026 · Q17[1]
   17 Convert $850{\text{ cm}}^3$ into litres.See it on the paper →
8. 0580/21 · May/June 2026 · Q21a[1]
   [Diagram: A cuboid ABCDEFGH with BF = 2 cm, BC = 6 cm, CD = 9 cm. NOT TO SCALE] The diagram shows a solid cuboid $ABCDEFGH$. $BF=2$ cm, $BC=6$ cm and $CD=9$ cm. (a) Calculate the volume of the cuboid.See it on the paper →
9. 0580/21 · May/June 2026 · Q21b[3]
   The diagram shows a solid cuboid $ABCDEFGH$. $BF=2\text{ cm}$, $BC=6\text{ cm}$ and $CD=9\text{ cm}$. (b) Calculate the surface area of the cuboid.See it on the paper →
10. 0580/22 · May/June 2026 · Q2b[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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11. 0580/22 · May/June 2026 · Q13[2]
    13 A sector of a circle has sector angle $90^{\circ }$ and radius $12$ cm. Calculate the arc length of the sector. Give your answer in terms of $\pi$.See it on the paper →
12. 0580/22 · May/June 2026 · Q16[2]
    16 The volume of a sphere is $500{\text{ cm}}^3$. Using the approximation of 3 for $\pi$, find an estimate for the radius of the sphere.See it on the paper →
13. 0580/22 · May/June 2026 · Q20[3]
    Two bottles are mathematically similar. The volume of the larger bottle is $216{\text{ cm}}^3$ and the volume of the smaller bottle is $27{\text{ cm}}^3$. The height of the larger bottle is $10\text{ cm}$ and the height of the smaller bottle is $h\text{ cm}$. Find the value of $h$.See it on the paper →
14. 0580/23 · May/June 2026 · Q7a[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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15. 0580/23 · May/June 2026 · Q14[2]
    14 A sphere has volume $36\pi {\text{ cm}}^3$. Find the radius of the sphere.See it on the paper →
16. 0580/23 · May/June 2026 · Q20[3]
    [Diagram: Two cylinders, A and B, labeled NOT TO SCALE. Cylinder A has height $h$ cm. Cylinder B has height $12$ cm.] The two cylinders, $A$ and $B$, are mathematically similar. The surface area of $A$ is $80{\text{ cm}}^2$ and the surface area of $B$ is $180{\text{ cm}}^2$. The height of $A$ is $h$ cm and the height of...See it on the paper →
17. 0580/31 · May/June 2026 · Q15a[3]
    15 (a) The diagram shows a cuboid. [Diagram: A cuboid with dimensions 8 cm, 3 cm, and 5 cm. Labelled "NOT TO SCALE".] Calculate the surface area of the cuboid.See it on the paper →
18. 0580/31 · May/June 2026 · Q15b[2]
    (b) A sphere has a radius of $6.4\text{ cm}$. Calculate the volume of the sphere. ${\text{cm}}^3$See it on the paper →
19. 0580/32 · May/June 2026 · Q11[2]
    11 A cuboid has length $10.8$ cm, width $3.7$ cm and height $4.6$ cm. Work out the volume of the cuboid. Give your answer correct to 1 decimal place.See it on the paper →
20. 0580/32 · May/June 2026 · Q24[1]
    24 A sphere has radius $6$ cm. Work out the surface area of the sphere. Give the units of your answer.See it on the paper →

What examiners said

Comprehensive responses • While the same comments apply as to part (a) candidates can improve by practising the required manipulation negatives indices. • A small proportion of candidates did work through to a fully correct answer. Limited responses • Many responses as numbers or in standard form were greater than 30 from multiplying by powers of 10. Candidates can improve by showing understandin...

— Examiner report, February/March 2026, 0580/12 Q24(b) (Cambridge)

Comprehensive responses • Many were able to give the correct surface area. • Some did not double at the relevant stage. Limited responses • Some found the volume. • Few made arithmetic errors, missed one or more faces, or used 10 + 3 + 4.

— Examiner report, February/March 2026, 0580/32 Q12 (Cambridge)

Comprehensive responses • Some candidates showed every step in the process to determine the given value for the capacity to the nearest litre. Limited responses • Most candidates showed the substitution of r = 40 into the correct volume formula for the sphere. • Few candidates showed the explicit step to convert cm3 to litres of division by 1000. • Few candidates showed the value of the capacity...

— Examiner report, February/March 2026, 0580/42 Q9(a) (Cambridge)