Mensuration: past paper questions

Where the questions come from

• Question 4May/June 2026, paper 21Structured2 marks

  The diagram shows a rectangle with width $6\text{ cm}$. The width of the rectangle is $\frac{1}{12}$ of the perimeter of the rectangle. Work out the length of the rectangle.

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• Question 4Oct/Nov 2025, paper 21Structured2 marks

  The area of a triangle is $12{\text{ cm}}^2$. The length of the base of the triangle is $8\text{ cm}$. Work out the height of the triangle.

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• Question 14Oct/Nov 2024, paper 21Structured4 marks

  Two solid steel statues are mathematically similar. The smaller statue has height $12\text{ cm}$ and the larger statue has height $15\text{ cm}$. The larger statue has a mass $2.5\text{ kg}$.

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• Question 22Oct/Nov 2023, paper 21Structured4 marksHas a diagram

  $ABCD$ is a rhombus with side length $13.6\text{ cm}$. Angle $ABC={41}^{\circ }$. $BAC$ is a sector of a circle with centre $B$.

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• Question 15May/June 2026, paper 21Structured4 marksHas a diagram

  Shape $A$ is one quarter of a circle with radius $t\text{ cm}$. Shape $B$ is a sector of a circle with radius $2t\text{ cm}$ and sector angle ${135}^{\circ }$. The area of shape $B$ is $k$ times the area of shape $A$.

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• Question 12Oct/Nov 2025, paper 21Structured4 marksHas a diagram

  The diagram shows a sector of a circle with centre $O$ and radius $9\text{ cm}$. The perimeter of the sector is $(18+2\pi )\text{ cm}$. Find the area of the sector.

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• Question 16Oct/Nov 2024, paper 21Structured4 marksHas a diagram

  The diagram shows a sphere of radius $6\text{ cm}$ and a cylinder of height $18\text{ cm}$ and radius $R\text{ cm}$. The volume of the sphere is equal to the volume of the cylinder. Calculate the curved surface area of the cylinder.

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• Question 4Oct/Nov 2023, paper 22Structured1 mark

  Change 62 000 millimetres into kilometres. Change 62 000 millimetres into kilometres.

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• Question 21May/June 2026, paper 21Structured9 marksHas a diagram

  The diagram shows a solid cuboid $ABCDEFGH$. $BF=2\text{ cm}$, $BC=6\text{ cm}$ and $CD=9\text{ cm}$. Calculate the volume of the cuboid.

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• Question 3Oct/Nov 2025, paper 22Structured2 marks

  A cuboid has length $6\text{ cm}$, width $5\text{ cm}$ and height $2.5\text{ cm}$. Work out the volume of the cuboid.

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• Question 5Oct/Nov 2024, paper 22Structured1 mark

  Convert $7.51{\text{ m}}^2$ into ${\text{cm}}^2$. Convert $7.51{\text{ m}}^2$ into ${\text{cm}}^2$.

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• Question 18Oct/Nov 2023, paper 22Structured4 marks

  A solid cylinder has radius $5\text{ cm}$ and height $8\text{ cm}$. Calculate the total surface area of the cylinder.

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• Question 2May/June 2026, paper 22Structured5 marks

  The diagram shows an accurate net of an open box in the shape of a cuboid. All the dimensions are whole numbers of centimetres. Find the total area of the net.

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• Question 23Oct/Nov 2025, paper 22Structured7 marksHas a diagram

  The diagram shows a major sector, $AOB$, of a circle. The sector angle is ${240}^{\circ }$ and the radius is $12\text{ cm}$. Show that the length of the major arc $AB$ is $16\pi \text{ cm}$.

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• Question 6Oct/Nov 2024, paper 22Structured2 marksHas a diagram

  The diagram shows a trapezium. The area of the trapezium is $42{\text{ cm}}^2$. Calculate the value of $x$.

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• Question 11Oct/Nov 2023, paper 23Structured4 marks

  A bronze sphere has radius $3.6\text{ cm}$. The density of bronze is $8.05{\text{ g/cm}}^3$. Find the mass of the sphere.

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• Question 13May/June 2026, paper 22Structured2 marks

  A sector of a circle has sector angle ${90}^{\circ }$ and radius $12\text{ cm}$. Calculate the arc length of the sector.

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• Question 4Oct/Nov 2025, paper 23Structured2 marksHas a diagram

  A rectangle measures $5\text{ cm}$ by $19\text{ cm}$. Two of these rectangles are joined to make a shape. Work out the perimeter of the shape.

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• Question 9Oct/Nov 2024, paper 22Structured3 marks

  Points $A$, $B$, $C$ and $D$ lie on a circle. $ABCD$ is a square with area $72{\text{ cm}}^2$. Calculate the area of the circle.

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• Question 16Oct/Nov 2023, paper 23Structured4 marks

  A cylinder with height $12.5\text{ cm}$ has a curved surface area of $105\pi {\text{ cm}}^2$. Calculate the volume of the cylinder.

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• Question 16May/June 2026, paper 22Structured2 marks

  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.

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• Question 19Oct/Nov 2025, paper 23Structured5 marksHas a diagram

  The diagram shows a circle, centre $O$, radius $12\text{ cm}$. Work out the area of the minor sector $AOB$.

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• Question 19Oct/Nov 2024, paper 22Structured7 marksHas a diagram

  A solid is made from a cylinder and a hemisphere, both of radius $4.3\text{ cm}$. The cylinder has length $11.9\text{ cm}$. Calculate the volume of the solid.

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• Question 8Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  The diagram shows a solid formed by joining two hemispheres and a cylinder. The radius of the large hemisphere is $5.4\text{ cm}$. The radius of the small hemisphere and the radius of the cylinder are both $3.6\text{ cm}$.

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• Question 14May/June 2026, paper 23Structured2 marks

  A sphere has volume $36\pi {\text{ cm}}^3$. Find the radius of the sphere.

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• Question 29Oct/Nov 2025, paper 23Structured5 marksHas a diagram

  In this question all measurements are in centimetres. Solid $A$ is made from a cylinder and a hemisphere, both of radius $2R$. The cylinder has height $5R$.

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• Question 6Oct/Nov 2024, paper 41Structured11 marksHas a diagram

  The diagram shows a field $ABCD$. A straight path $AC$ goes across the field. Show that $AC=1028\text{ m}$, correct to the nearest metre.

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• Question 4Oct/Nov 2023, paper 42Structured12 marksHas a diagram

  The diagram shows a sector of a circle that is made into a cone by joining $OA$ to $OB$. The sector angle is $x^{\circ }$ and the radius of the sector is $7.5\mathrm{c}\mathrm{m}$. The base radius of the cone is $1.5\mathrm{c}\mathrm{m}$.

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• Question 18May/June 2026, paper 23Structured6 marksHas a diagram

  The diagram shows a rectangle. The shaded area is $30{\text{ cm}}^2$. Show that $x^2+16x-36=0$.

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• Question 9Oct/Nov 2025, paper 41Structured2 marks

  An athlete runs at a speed of $9.5\text{ m/s}$. Convert this speed into $\text{km/h}$. An athlete runs at a speed of $9.5\text{ m/s}$.

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