AQA · Mathematics · 8300

GCSE Maths: Volume: Frustum

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Volume: Frustum (Corbettmaths Video 360), 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 a frustum of a cone?

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    The solid left when a smaller cone is removed from the top of a cone by a cut parallel to the base.

  2. How do you calculate the volume of a frustum?

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    Volume of the whole (large) cone or pyramid minus the volume of the smaller cone or pyramid removed from the top.

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

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

  4. What is the formula for the volume of a pyramid?

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    V = ⅓ × base area × perpendicular height.

  5. Mass = ? × volume.

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    density

  6. How many grams are in one kilogram?

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    1000 g = 1 kg, so divide a mass in grams by 1000 to convert to kilograms.

  7. If two similar solids have linear scale factor k, what is their volume scale factor?

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    k³ — volumes of similar solids scale by the cube of the linear scale factor.

  8. A frustum of height 20 cm is cut from a cone of height 24 cm. What is the height of the removed cone?

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    24 − 20 = 4 cm.

  9. A pyramid of height 60 cm is cut 15 cm below its apex. What fraction of the original volume is the frustum?

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    63/64 — the small pyramid has linear scale factor ¼, so volume (¼)³ = 1/64, leaving 1 − 1/64 = 63/64.

  10. How do you find the mass of a solid made from two different metals?

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    Find the volume of each part separately, multiply each by its own density, then add the two masses.

  11. What unit is density measured in when mass is in grams and volume in cm³?

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    g/cm³.

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