Surface area and volume: past paper questions

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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 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 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 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 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 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 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 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 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 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 14Oct/Nov 2025, paper 41Structured10 marks

  A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8\text{ cm}$.

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• Question 9Oct/Nov 2024, paper 41Structured12 marksHas a diagram

  $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. Work out the volume of the cuboid.

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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 16May/June 2026, paper 42Structured9 marksHas a diagram

  $ABCDE$ is a square-based pyramid. $EC$ and $BD$ intersect at $F$. $AF$ is perpendicular to the base $BCDE$.

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• Question 13May/June 2025, paper 21Structured8 marksHas a diagram

  The diagram shows solid $A$ and solid $B$. Solid $A$ is made from a hemisphere and a cone each with radius $6\text{ cm}$. The cone has sloping edge $10\text{ cm}$.

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• Question 4Oct/Nov 2024, paper 43Structured15 marksHas a diagram

  A box contains 50 cuboids. Each cuboid has a mass of $135\text{ g}$. The total mass of the cuboids and the box is $7\text{ kg}$.

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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 21May/June 2026, paper 43Structured5 marksHas a diagram

  The diagram shows a frustum. Calculate the volume of the frustum.

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• Question 16May/June 2025, paper 22Structured4 marksHas a diagram

  The diagram shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and the cylinder is $6\text{ cm}$. The height of the cylinder is $5\text{ cm}$.

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• Question 4May/June 2024, paper 23Structured2 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.

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• Question 6May/June 2023, paper 21Structured2 marks

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

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• Question 20May/June 2025, paper 41Structured9 marksHas a diagram

  The diagram shows a pyramid $OABCD$. The pyramid has a square base, $ABCD$, with sides $10.5\text{ cm}$. The vertex $O$ is vertically above the centre of the base, $M$.

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• Question 7May/June 2024, paper 41Structured15 marksHas a diagram

  The diagram shows a box in the shape of a cuboid. The box is open at the top. Work out the surface area of the inside of the open box.

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• Question 3May/June 2023, paper 23Structured3 marksHas a diagram

  Find the total surface area of the cuboid.

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• Question 6May/June 2025, paper 42Structured3 marks

  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.

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• Question 4May/June 2024, paper 42Structured15 marksHas a diagram

  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 water. Calculate the volume of water in the tank.

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• Question 16May/June 2023, paper 23Structured3 marks

  The volume of a cylinder is $1970{\text{ cm}}^3$. The height of the cylinder is $12.8\text{ cm}$. Calculate the radius of the cylinder.

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