Surface area and volume: past paper questions

Where the questions come from

• Question 14May/June 2026, paper 13Structured5 marksHas a diagram

  The diagram shows a right-angled triangular prism. On the $1{\text{ cm}}^2$ grid, complete the net of this prism.

  Try this question
• Question 13Oct/Nov 2025, paper 31Structured6 marksHas a diagram

  The surface area of a solid cube is $121.5{\text{ cm}}^2$. Calculate the length of the side of the cube.

  Try this question
• Question 10Oct/Nov 2024, paper 13Structured2 marks

  The surface area of a cube is $121.5{\text{ cm}}^2$. Calculate the length of one side of the cube.

  Try this question
• Question 8Oct/Nov 2023, paper 13Structured2 marks

  The surface area of a cube is $73.5{\text{ cm}}^2$. Find the length of one side of the cube.

  Try this question
• Question 15May/June 2026, paper 31Structured5 marksHas a diagram

  The diagram shows a cuboid. Calculate the surface area of the cuboid.

  Try this question
• Question 19Oct/Nov 2025, paper 32Structured3 marksHas a diagram

  The diagram shows a cylinder and a cube. The cylinder has the same volume as the cube. Find the value of x. The diagram shows a cylinder and a cube.

  Try this question
• Question 7Oct/Nov 2024, paper 31Structured11 marksHas a diagram

  Find the perimeter of the triangle.

  Try this question
• Question 4Oct/Nov 2023, paper 31Structured9 marksHas a diagram

  The diagram shows a cuboid. On the $1{\text{ cm}}^2$ grid, complete the net of the cuboid.

  Try this question
• Question 11May/June 2026, paper 32Structured2 marks

  A cuboid has length 10.8 cm, width 3.7 cm and height 4.6 cm. Work out the volume of the cuboid.

  Try this question
• Question 8Oct/Nov 2024, paper 31Structured12 marks

  The diagram shows the net of a solid. Write down the mathematical name of the solid.

  Try this question
• Question 2Oct/Nov 2023, paper 32Structured10 marks

  Write down the mathematical name for this polygon.

  Try this question
• Question 24May/June 2026, paper 32Structured3 marks

  A sphere has radius 6 cm. Work out the surface area of the sphere.

  Try this question
• Question 11May/June 2025, paper 11Structured1 mark

  Calculate the volume of a cube with side length 3 cm.

  Try this question
• Question 4Oct/Nov 2024, paper 32Structured13 marksHas a diagram

  Calculate the volume of a cylinder with radius $7.8\text{ cm}$ and height $15\text{ cm}$.

  Try this question
• Question 5Oct/Nov 2023, paper 33Structured12 marksHas a diagram

  Zena records the number of letters she posts on each of 12 days. $$373871065172$$ Write down the mode.

  Try this question
• Question 26May/June 2026, paper 33Structured4 marksHas a diagram

  The diagram shows a sphere and a cone. The radius of the sphere is $3.6\text{ cm}$. The radius of the cone is $r\text{ cm}$ and the slant height is $8\text{ cm}$.

  Try this question
• Question 10May/June 2025, paper 12Structured5 marks

  A cuboid has length $5\text{ cm}$, width $2\text{ cm}$ and height $3\text{ cm}$. Draw a net of the cuboid on the $1{\text{ cm}}^2$ grid.

  Try this question
• Question 1Oct/Nov 2024, paper 33Structured13 marksHas a diagram

  Li has $20. A box of cereal costs $2.29 . Work out the maximum number of boxes of cereal that Li can buy.

  Try this question
• Question 13May/June 2023, paper 11Structured2 marks

  Calculate the volume of a sphere with diameter $4.8\text{ cm}$.

  Try this question
• Question 8May/June 2025, paper 13Structured6 marks

  The diagram shows two faces of a net of a cuboid on a $1{\text{ cm}}^2$ grid. Complete the statement.

  Try this question
• Question 10May/June 2024, paper 11Structured4 marksHas a diagram

  The total surface area of this cuboid is $369{\text{ cm}}^2$. Work out the value of $h$.

  Try this question
• Question 8May/June 2023, paper 13Structured3 marksHas a diagram

  Find the total surface area of the cuboid.

  Try this question
• Question 9May/June 2025, paper 13Structured3 marksHas a diagram

  The diagram shows the net of a square-based pyramid. The perpendicular height of each triangle is $4\text{ cm}$. The base has side length $5\text{ cm}$.

  Try this question
• Question 16May/June 2024, paper 12Structured5 marks

  A circle has an area of $36\pi {\text{ cm}}^2$. Find the circumference of the circle.

  Try this question
• Question 4May/June 2023, paper 31Structured9 marksHas a diagram

  The diagram shows the net of a solid on a $1{\text{ cm}}^2$ grid. When the net is folded to make the solid, point $C$ will join with point $A$. Write down which other point will join with point $A$.

  Try this question
• Question 17May/June 2025, paper 31Structured3 marks

  The volume of a cylinder is $863.5{\text{ cm}}^3$. The height of the cylinder is $12.3\text{ cm}$. Find the radius of the cylinder.

  Try this question
• Question 7May/June 2024, paper 13Structured2 marks

  The base of a cuboid measures $10\text{ cm}$ by $7\text{ cm}$. The volume of the cuboid is $280{\text{ cm}}^3$. Calculate the height of the cuboid.

  Try this question
• Question 5May/June 2023, paper 32Structured11 marksHas a diagram

  This rectangle has an area of $12{\text{ cm}}^2$ and a perimeter of $16\text{ cm}$. This shape is made from six of these rectangles. Find the area and perimeter of this shape.

  Try this question
• Question 25May/June 2025, paper 31Structured3 marks

  A bar of gold in the shape of a cuboid has dimensions $2\text{ cm}$ by $4\text{ cm}$ by $6.5\text{ cm}$. The density of gold is $19.32{\text{ g/cm}}^3$. Calculate the mass of this bar of gold.

  Try this question
• Question 23May/June 2024, paper 13Structured5 marksHas a diagram

  The diagram shows a spherical tank with radius $0.5\text{ m}$ and a cylindrical jug with diameter $24\text{ cm}$ and height $32\text{ cm}$. The tank is full of water. Calculate how many times the jug can be completely filled with water from the tank.

  Try this question