AQA · Mathematics · 8300
GCSE Maths: Surface area: frustum
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Surface area: frustum (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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What is a frustum of a cone?
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A frustum is the shape formed by removing a small cone from the top of a larger cone.
What three surface areas must be calculated to find the total surface area of a frustum?
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The curved surface area, the area of the top circular face, and the area of the bottom circular face.
How is the curved surface area of a frustum calculated?
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Subtract the curved surface area of the small removed cone from the curved surface area of the large original cone.
The curved surface area of a cone is given by the formula π × r × ?, where r is the radius and l is the slant height.
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l
How do you find the total slant height of the original cone when given a frustum?
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Add the slant height of the small removed cone to the slant height of the frustum.
The area of a circle is given by the formula π × ?, where r is the radius.
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r²
In a frustum problem, why are the radii of the two cones proportional to their slant heights?
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Because the small cone and large cone are similar shapes (one is a scaled version of the other), so corresponding dimensions are in the same ratio.
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