GCSE · Perimeter, area & volume

Volume of prisms, cylinders, cones & spheresExam-style questions

Why a prism's volume is cross-section × length, why a cylinder is just a circular prism, where the ⅓ in pyramid and cone formulas fits in, spheres and hemispheres, and litres.

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19 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    A solid metal cube has edges of length 1212 cm.

    The cube is melted down and all of the metal is used to make a solid square-based pyramid.

    The base of the pyramid is a square of side 1818 cm.

    Work out the perpendicular height of the pyramid.

    (3 marks)
    Level 4 · 3 marksTry it
  2. 2
    A wooden post is in the shape of a cylinder with a cone at one end.120 cmr cm15 cmVolume of cone =13πr2h= \frac{1}{3}\pi r^2 h

    The cylinder and the cone both have radius rr cm.

    The length of the cylinder is 120120 cm.

    The height of the cone is 1515 cm.

    The volume of the post is 2000π2000\pi cm³

    Work out the value of rr.

    You must show all your working.

    (4 marks)
    Level 4 · 4 marksTry it
  3. 3
    The diagram shows a toy made from a cone on top of a hemisphere.3 cm8 cmDiagram NOT accurately drawn

    The cone and the hemisphere each have radius 33 cm. The height of the cone is 88 cm.

    Volume of a cone =13πr2h= \frac{1}{3}\pi r^2 h · Volume of a sphere =43πr3= \frac{4}{3}\pi r^3

    Work out the volume of the toy. Give your answer correct to 3 significant figures.
    Level 4 · 4 marksTry it
  4. 4
    A sphere has volume 972π972\pi cm³.

    Volume of a sphere =43πr3= \frac{4}{3}\pi r^3

    Work out the radius of the sphere.
    Level 4 · 3 marksTry it
  5. 5
    A cylinder with internal radius 55 cm contains water to a depth of 2424 cm.

    All the water is poured into an empty tank in the shape of a cuboid. The base of the tank measures 1515 cm by 1010 cm. The water does not overflow.

    Work out the depth of the water in the tank. Give your answer correct to 1 decimal place.
    Level 4 · 4 marksTry it

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