AQA · Mathematics · 8300

GCSE Maths: Volume: cone

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Volume: cone (Corbettmaths Video 359), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

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  1. What is the formula for the volume of a cone?

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    V = ⅓πr²h, where r is the base radius and h is the perpendicular height.

  2. The volume of a cone is ? of the volume of a cylinder with the same base radius and height.

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    one third

  3. What is the volume of a cone with base radius 5 cm and perpendicular height 9 cm, to 1 d.p.?

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    235.6 cm³ (V = ⅓ × π × 5² × 9 = 75π).

  4. A cone has base diameter 8 cm. What radius do you use in the volume formula?

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    4 cm — the radius is half the diameter.

  5. In terms of π, what is the volume of a cone with base diameter 18 cm and height 20 cm?

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    540π cm³ (radius 9 cm: ⅓ × π × 81 × 20).

  6. How do you find a cone's perpendicular height from its slant height and radius?

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    Use Pythagoras: h = √(l² − r²), since the height, radius and slant height form a right-angled triangle.

  7. A cone has radius 5 cm and slant height 13 cm. What is its perpendicular height?

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    12 cm (√(13² − 5²) = √144).

  8. What is the formula for the volume of a hemisphere?

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    V = ⅔πr³ (half the volume of a sphere).

  9. How do you calculate the volume of a frustum of a cone?

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    Volume of the large (full) cone minus the volume of the smaller cone removed from the top.

  10. How do you find the missing height of the full cone when only the frustum dimensions are given?

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    Use similar triangles: the ratio radius : height is the same for the small cone and the full cone.

  11. How many cubic centimetres are in 1 litre?

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    1000 cm³.

  12. A cone and a hemisphere share radius x and have equal volumes. What is the cone's height h in terms of x?

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    h = 2x (from ⅓πx²h = ⅔πx³).

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