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Prisms and cylinders – practice for Years 7–9

Sample questions on Prisms and cylinders with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 7–9
Curriculum area
Geometry and measures

Question types: Volume and surface area of prisms and cylinders

Rule: Prisms and cylinders

Volume of a prism and of a cylinder: V = base area × height; cylinder: V = π × r² × h.

Surface area = 2 bases + the sides: prism sides = base perimeter × height, cylinder side = 2 × π × r × h.

Example: Cylinder r = 5 cm, h = 9 cm: V = 3.14 × 25 × 9 = 706.5 cm³

Watch out: The surface area has two bases: don’t forget either of them.

Sample questions

  1. Question 1 Easy

    A prism has a base that is a right-angled triangle with legs of 6 cm and 3 cm. The height of the prism is 5 cm. Work out its volume.

    Show the solution
    Answer: 45 cm³

    How it works: Base area = 6 × 3 ÷ 2 = 9 cm²; V = 9 × 5 = 45 cm³

  2. Question 2 Normal

    A barrel in the shape of a cylinder has an inside radius of 4 dm and a height of 15 dm. How many litres of water does it hold? Use π ≈ 3.14.

    Show the solution
    Answer: 753.6 l

    How it works: V = π × r² × h = 3.14 × 16 × 15 = 753.6 dm³ = 753.6 l

  3. Question 3 Hard

    A cylinder has base radius r = 8 cm and height h = 7 cm. Work out its surface area. Use π ≈ 3.14.

    Show the solution
    Answer: 753.6 cm²

    How it works: SA = 2 × π × r² + 2 × π × r × h = 2 × 3.14 × 8 × (8 + 7) = 753.6 cm²

Related topics

All Maths topics

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