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Maths (Higher)
2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Starter quiz

  • A __________ is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.
    • frustum  ✓
    • hemi-cone
    • semi-cone
  • The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.
    The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.
    • a
      ⇔
      16 cm ✓
    • b
      ⇔
      4 cm ✓
    • c
      ⇔
      21 cm ✓
  • The diagram shows a side elevation of a frustum. Find the volume of the large cone that the frustum is cut from. Give your answer correct to 3 significant figures.
    The diagram shows a side elevation of a frustum. Find the volume of the large cone that the frustum is cut from. Give your answer correct to 3 significant figures.
    • 219 000 cm³
    • 309 000 cm³
    • 803 000 cm³  ✓
    • 3 210 000 cm³
  • The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.
    The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.
    • 214 000 cm³
    • 314 000 cm³
    • 414 000 cm³
    • 494 000 cm³  ✓
    • 1 110 000 cm³
  • A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 12 cm. The height of the small cone is <span class="blank">______</span> cm.
    A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 12 cm. The height of the small cone is ______ cm.
    • '80' ✓
  • The diagram shows a large cone with a frustum of height 20 cm and a small cone. The radius of the frustum base is 15 cm and the radius of its top is 12 cm. The volume of the frustum is <span class="blank">______</span>𝜋 cm³.
    The diagram shows a large cone with a frustum of height 20 cm and a small cone. The radius of the frustum base is 15 cm and the radius of its top is 12 cm. The volume of the frustum is ______𝜋 cm³.
    • '3660' ✓
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