Surface area and volume: past paper questions

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• Question 19May/June 2026, paper 12Structured6 marksHas a diagram

  The diagram shows a solid hemisphere and a solid cylinder. All the lengths are in centimetres. The radius of the hemisphere is $3x$.

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• Question 12Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  The diagram shows an empty container. The container is a cuboid of width $10\text{ cm}$, length $8\text{ cm}$ and height $9\text{ cm}$. Water drips into the container at a rate of 6 millilitres per second.

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• Question 6Oct/Nov 2024, paper 21Structured10 marksHas a diagram

  [Volume of sphere $=\frac{4}{3}\pi r^3$] The diagram shows a sphere inside a cube. The sphere touches all 6 faces of the cube. The volume of the cube is $343{\text{ cm}}^3$.

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• Question 9Oct/Nov 2023, paper 21Structured14 marksHas a diagram

  The diagram shows a triangular prism. $AB=6\text{ cm}$, angle $BAC={55}^{\circ }$ and the length of the prism is $20\text{ cm}$. The area of triangle $ABC$ is $34.4{\text{ cm}}^2$.

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• Question 23May/June 2026, paper 22Structured12 marksHas a diagram

  The diagram shows a sector of a circle with centre $O$ and radius $9.1\text{ cm}$. The length of the major arc $AB$ is $44\text{ cm}$. Find the angle of the major sector $AOB$.

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• Question 17Oct/Nov 2025, paper 11Structured7 marksHas a diagram

  The diagram shows a prism. The cross-section of the prism is an isosceles triangle with sides $13\text{ cm}$, $13\text{ cm}$ and base $10\text{ cm}$. The length of the prism is $3\text{ cm}$.

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• Question 3Oct/Nov 2024, paper 22Structured10 marksHas a diagram

  The diagram shows a tank. The tank is a cuboid with length $1.2\text{ m}$, width $0.6\text{ m}$ and height $h\text{ m}$. The volume of the tank is $1.8{\text{ m}}^3$.

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• Question 10Oct/Nov 2023, paper 22Structured12 marksHas a diagram

  [Volume of a cone $=\frac{1}{3}\pi r^{2}h$] [Curved surface area of a cone $=\pi rl$] A solid is formed from a large cone with a small cone removed from the centre. The small cone is mathematically similar to the large cone.

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• Question 24May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a solid cuboid. All the lengths are in centimetres. The volume of the cuboid is $720{\text{ cm}}^3$.

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• Question 18Oct/Nov 2025, paper 12Structured5 marksHas a diagram

  The diagram shows a solid cylinder and a solid hemisphere. The radius of the cylinder is equal to the radius of the hemisphere. The volume of the cylinder is equal to the volume of the hemisphere.

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• Question 21May/June 2024, paper 11Structured4 marksHas a diagram

  Prism $A$ and prism $B$ are mathematically similar. In the diagram, the cross-sections of the prisms are shaded. The volume of prism $A$ is $5000{\text{ cm}}^3$.

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• Question 9May/June 2023, paper 12Structured3 marksHas a diagram

  The diagram shows a triangular prism. The cross-section is a right-angled isosceles triangle. Write down the number of planes of symmetry of the prism.

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• Question 3Oct/Nov 2025, paper 21Structured3 marks

  In this question, all lengths are in centimetres. The diagram shows the net of a cuboid. Find the total surface area of the cuboid.

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• Question 7May/June 2024, paper 21Structured10 marksHas a diagram

  A cuboid has dimensions 5 cm by 12 cm by $h$ cm. The volume of the cuboid is $480{\text{ cm}}^3$. Calculate the value of $h$.

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• Question 1May/June 2023, paper 21Structured9 marksHas a diagram

  A cuboid has dimensions $x\text{ cm}$, $(5-x)\text{ cm}$ and $15\text{ cm}$. Show that the equation for the volume of the cuboid, $y{\text{ cm}}^3$, is $y=75x-15x^2$.

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• Question 3May/June 2025, paper 12Structured3 marks

  The area of one face of a cube is $9{\text{ cm}}^2$. On the $1\text{ cm}$ grid, draw an accurate net of the cube.

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• Question 8May/June 2024, paper 22Structured15 marksHas a diagram

  [Volume of a cone $=\frac{1}{3}\pi r^{2}h$] [Volume of a sphere $=\frac{4}{3}\pi r^3$] [Curved surface area of cone $=\pi rl$] [Surface area of a sphere $=4\pi r^2$] A solid is formed by placing a cone on top of a hemisphere.

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• Question 11May/June 2023, paper 21Structured9 marksHas a diagram

  The diagram shows an open container on a horizontal surface. The container is a prism with trapezium $ABCD$ as its cross-section. $AB=28\text{ cm}$, $DC=24\text{ cm}$, $AD=16\text{ cm}$ and $BF=29\text{ cm}$.

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• Question 21May/June 2025, paper 22Structured11 marksHas a diagram

  The diagram shows a solid formed by joining a cone to a hemisphere. The diameter of the cone is $14\text{ cm}$ and the diameter of the hemisphere is $14\text{ cm}$. The total height of the solid is $24\text{ cm}$.

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• Question 8May/June 2023, paper 22Structured11 marksHas a diagram

  The length of the rectangle $R$ is twice its width. Rectangle $R$ has a perimeter of $20.4\text{ cm}$. Find the length and width of the rectangle $R$.

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