AQA · Mathematics · 8300

GCSE Maths: Surface area: cone

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Surface area: cone (Corbettmaths Video 314), 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 formula gives the curved surface area of a cone?

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    πrl, where r is the base radius and l is the slant height.

  2. What formula gives the total surface area of a cone?

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    πrl + πr², where r is the base radius and l is the slant height (curved surface plus base area).

  3. How do you find the slant height of a cone given the perpendicular height and radius?

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    Use Pythagoras' theorem: l² = h² + r², where l is slant height, h is perpendicular height, and r is radius.

  4. A cone has base radius 3 cm, perpendicular height 4 cm, and slant height 5 cm. What is its surface area?

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    24π cm² (calculated as π × 3 × 5 + π × 3² = 15π + 9π).

  5. A cone has base radius 10 cm and slant height 18 cm. What is its surface area in terms of π?

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    280π cm² (calculated as π × 10 × 18 + π × 10² = 180π + 100π).

  6. A cone has vertical height 20 cm and base radius 4.5 cm. What is the slant height?

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    Approximately 20.5 cm (using Pythagoras: l = √(20² + 4.5²)).

  7. What is a frustum of a cone?

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    A solid shape made by cutting a small cone from the top of a larger cone.

  8. When calculating the surface area of a cone on top of a cylinder, which surface is NOT counted?

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    The circular base of the cone (and the top of the cylinder), because they are joined together and not part of the external surface.

  9. A cone has base radius 2 cm and perpendicular height 5 cm. What steps are needed to find its surface area?

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    First find slant height using Pythagoras (l = √(2² + 5²) = √29 cm), then calculate πrl + πr² = π(2)(√29) + π(2²) = 2π√29 + 4π cm².

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