AQA · Mathematics · 8300

GCSE Maths: Volume: pyramid

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Volume: pyramid (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 the formula for the volume of a pyramid?

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    V = ⅓ × base area × perpendicular height.

  2. Volume of a pyramid with base area 60 cm² and perpendicular height 7 cm?

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    140 cm³ (⅓ × 60 × 7).

  3. Volume of a square-based pyramid, base side 15 cm, perpendicular height 10 cm?

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    750 cm³ (⅓ × 15² × 10 = ⅓ × 225 × 10).

  4. How do you find the area of an equilateral triangle with side length a?

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    Area = ½ × a × a × sin 60° = (√3/4) a².

  5. Volume of a pyramid whose base is an equilateral triangle of side 6 cm and whose perpendicular height is 4 cm?

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    ≈ 20.8 cm³. Base area = ½ × 6 × 6 × sin 60° ≈ 15.59 cm²; V = ⅓ × 15.59 × 4.

  6. How do you calculate the volume of a frustum of a pyramid?

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    Volume of the whole (large) pyramid minus the volume of the small pyramid removed from the top.

  7. A square pyramid (base 8 cm, height 10 cm) is cut to leave a top pyramid of base 4 cm. Volume of the frustum?

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    ≈ 187 cm³. Whole: ⅓ × 64 × 10 = 213.3; top pyramid has height 5 cm (scale factor ½): ⅓ × 16 × 5 = 26.7; 213.3 − 26.7 = 186.7.

  8. How do you find the perpendicular height of a pyramid given its volume and base area?

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    h = 3V ÷ base area (rearranging V = ⅓ × base area × h).

  9. How do you find the volume of a solid from its mass and density?

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    Volume = mass ÷ density (e.g. 1705.6 g ÷ 2.6 g/cm³ = 656 cm³).

  10. Square-based pyramid, base side 16 cm, slant edge from a base corner to the apex 20 cm: what is its volume?

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    ≈ 1407 cm³. Half-diagonal of base = 8√2 ≈ 11.31 cm; height = √(20² − (8√2)²) = √272 ≈ 16.49 cm; V = ⅓ × 256 × 16.49.

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