Mensuration: past paper questions

Real questions on mensuration

The newest 20 of 68 written questions. Open one to see it on the real paper.

1. 0980/41 · October/November 2025 · Q14a[1]
   14 A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8\text{ cm}$. (a) Show that the volume of the sphere is $\frac{256}{3}\pi {\text{ cm}}^3$.See it on the paper →
2. 0980/41 · October/November 2025 · Q14b[3]
   A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is 8 cm. (b) Calculate the percentage of the cube that is not occupied by the sphere.See it on the paper →
3. 0980/41 · October/November 2025 · Q14c[2]
   A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8\text{ cm}$. (c) The density of the metal of the sphere is $7.86{\text{ g/cm}}^3$. Calculate the mass of the sphere. Give your answer in kilograms. [Density = mass $÷$ volume]See it on the paper →
4. 0980/41 · October/November 2025 · Q14d[4]
   A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8$ cm. (d) The sphere is melted down and made into a solid cylinder with radius $3.1$ cm. Calculate the **total** surface area of the cylinder.See it on the paper →
5. 0980/22 · May/June 2025 · Q16[4]
   16 [Diagram: A solid composed of a hemisphere on top of a cylinder. The radius of the hemisphere and cylinder is labelled 6 cm. The height of the cylinder is labelled 5 cm. The text "NOT TO SCALE" is present.] The diagram shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and th...See it on the paper →
6. 0980/32 · May/June 2025 · Q23[4]
   A sphere has radius 8 cm. A cone has radius 8 cm and height $h$. The sphere and the cone have the same volume. Work out the height, $h$, of the cone.See it on the paper →
7. 0980/42 · May/June 2025 · Q6[3]
   A solid wooden cone has base radius $4\text{ cm}$ and height $12\text{ cm}$. The density of the wood is $0.74{\text{ g/cm}}^3$. Calculate the mass of the cone. [Density = Mass ÷ Volume]See it on the paper →
8. 0980/21 · October/November 2024 · Q16[4]
   16 [Diagram: A sphere with a radius of 6 cm indicated by an arrow from the center to the edge. Next to it, a cylinder with radius $R$ cm and height 18 cm. The text "NOT TO SCALE" is written to the right of the cylinder.] The diagram shows a sphere of radius 6 cm and a cylinder of height 18 cm and radius $R$ cm. The vol...See it on the paper →
9. 0980/31 · October/November 2024 · Q7d[2]
   (d) Calculate the volume of a sphere with diameter $5.25$ cm. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$.]See it on the paper →
10. 0980/31 · October/November 2024 · Q8a(ii)[2]
    8 (a) The diagram shows the net of a solid. [Diagram: A net of a cuboid consisting of a row of four squares and one square attached to the top of the second square from the left. The top edge of the top square is labelled $10\text{ cm}$. The top edge of the leftmost square in the row is labelled $x\text{ cm}$. The left...See it on the paper →
11. 0980/31 · October/November 2024 · Q8a(iii)[1]
    8 (a) The diagram shows the net of a solid. [Diagram: A net of a cuboid consisting of a row of four rectangles and one rectangle attached above the second rectangle from the left. The top rectangle has a top edge labelled $10\text{ cm}$. The leftmost rectangle in the row has a top edge labelled $x\text{ cm}$ and a left...See it on the paper →
12. 0980/31 · October/November 2024 · Q8a(iv)[2]
    (a) The diagram shows the net of a solid. [Diagram: A net of a cuboid consisting of a row of three squares and one square attached to the top of the middle square. The top square has a top edge labelled $10\text{ cm}$. The leftmost square in the row has a left edge labelled $x\text{ cm}$ and a top edge labelled $x\text...See it on the paper →
13. 0980/41 · October/November 2024 · Q9a[1]
    [Diagram: A cuboid labelled $ABCDEFGH$. $AB=10\text{ cm}$, $BC=8\text{ cm}$, $CG=17\text{ cm}$. NOT TO SCALE] $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. (a) Work out the volume of the cuboid.See it on the paper →
14. 0980/41 · October/November 2024 · Q9b[3]
    [Diagram: A cuboid labeled $ABCDEFGH$. The bottom face is $ABCD$ and the top face is $EFGH$. The edge $AB$ is labeled $10\text{ cm}$. The edge $BC$ is labeled $8\text{ cm}$. The vertical edge $CG$ is labeled $17\text{ cm}$. The text "NOT TO SCALE" is present.] $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC = 8\...See it on the paper →
15. 0980/12 · May/June 2024 · Q16b[2]
    16 A circle has an area of $36\pi {\text{ cm}}^2$. (b) The circle forms the base of a cylinder with height $h$ cm. The volume of the cylinder is $540\pi {\text{ cm}}^3$. Work out the value of $h$.See it on the paper →
16. 0980/32 · May/June 2024 · Q7a[3]
    The area of some land is in the ratio park : gardens : playground = $11:2:3$. The park has an area of $4620{\text{ m}}^2$. (a) Work out the area of the gardens and the area of the playground.See it on the paper →
17. 0980/32 · May/June 2024 · Q7b(i)[1]
    The area of some land is in the ratio park : gardens : playground = $11:2:3$. The park has an area of $4620{\text{ m}}^2$. (b) The park area of $4620{\text{ m}}^2$ is made up of paths and grassland. $18\%$ of the park area is paths. (i) Show that the grassland area is $3788.4{\text{ m}}^2$.See it on the paper →
18. 0980/32 · May/June 2024 · Q8a(i)[1]
    [Diagram: A plan of a room $ABCDE$. $AB$ is horizontal at the top, length $3.6\text{ m}$. $BC$ is vertical on the left, length $4.7\text{ m}$. $CD$ is horizontal at the bottom, length $5.5\text{ m}$. $DE$ is vertical on the right, length $1.7\text{ m}$. $AE$ is a slanted line connecting $A$ and $E$. Right angle symbols...See it on the paper →
19. 0980/32 · May/June 2024 · Q8c[2]
    The diagram shows a plan, $ABCDE$, of the floor of a room in Jo’s house. $F$ is a point inside the room. [Diagram: A polygon $ABCDE$ with right angles at $B$, $C$, and $D$. $AB$ is horizontal with length $3.6\text{ m}$. $BC$ is vertical with length $4.7\text{ m}$. $CD$ is horizontal with length $5.5\text{ m}$. $DE$ is...See it on the paper →
20. 0980/42 · May/June 2024 · Q4a(i)[3]
    [Diagram: A half-cylinder tank lying horizontally. The semi-circular cross-section has a radius of 12 cm. The length of the tank is 1 m. Labelled "NOT TO SCALE".] The diagram shows a tank in the shape of a half-cylinder of radius 12 cm and length 1 metre. The tank is fixed horizontally and is completely filled with wat...See it on the paper →

What examiners said

Many made use of the formula sheet effectively, although a few chose the incorrect formulae. Most candidates correctly substituted the radius into one of the equations, gaining the first mark. Many got no further. The number of candidates who equated the two formulae was limited and for some, errors in substitution or further processing meant that they did not reach a correct equation linking the...

— Examiner report, May/June 2025, 0980/32 Q23 (Cambridge)

Candidates were very well prepared for this question, and the majority were able to score full marks for a correct answer. Many candidates either knew the correct formula for the volume of a cone or made use of the provided formula and then substituted correctly to find the required volume. Some candidates then worked with the accurate volume, 64π, while others used a decimal approximation in the...

— Examiner report, May/June 2025, 0980/42 Q6 (Cambridge)

Unfortunately, very few candidates related this part of the question to the stem giving the area as 36. Those who did see the connection and realised that height was volume divided by area often gained the marks.

— Examiner report, May/June 2024, 0980/12 Q16(b) (Cambridge)