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Surface area of a frustum of a cone

The starter and exit quiz of the lesson “Surface area of a frustum of a cone”, from the unit “2D and 3D shape: surface area and volume (pyramids, spheres and cones)” (Year 11 Maths) by Oak National Academy.

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Oak National Academy

12 questions

  1. A __________ is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.
  2. The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.
  3. 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.
  4. The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.
  5. 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.
  6. 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.
  7. A circular cone has ___ surfaces.
  8. The area of the curved surface of this frustum is ___𝜋 cm². Leave your answer in terms of 𝜋.
  9. The total surface area of this frustum is ___𝜋 cm². Leave your answer in terms of 𝜋.
  10. Work out the length of the side marked x on this frustum.
  11. Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.
  12. The total surface area of this frustum is ___𝜋 cm². Leave your answer in terms of 𝜋.

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Surface area of a frustum of a cone · Examplary