Frustums & truncated solids
AQA GCSE Maths revision on Frustums & truncated solids. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
What is the shape of the cross-section produced when a cone is cut by a plane parallel to its base?
- A) A circle represents the cross-section area.
- B) A square represents the cross-section area.
- C) A sector represents the cross-section area.
- D) A triangle represents the cross-section area.
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Answer: A circle represents the cross-section area.
The correct answer is a circle. When a plane is parallel to the base of a cone, the resulting cross-section is always a smaller version of the circular base. A common misconception is to assume it creates a triangle, which occurs only if the plane passes through the apex.
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Question 2
If a large pyramid has a height of 10 cm and a smaller pyramid is removed from the top to leave a frustum, what is the height of the smaller pyramid if the scale factor of the cut is 0.4?
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Answer: 4
The correct answer is 4. By multiplying the original height of 10 cm by the scale factor of 0.4, you find the height of the removed top section. This relationship is derived from the properties of similar solids.
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Question 3
Which expression correctly represents the volume of a frustum with a large base area A, small base area a, and height h?
- A) One third height times sum of A plus a plus root Aa.
- B) One third height times sum of A plus a plus root Aa.
- C) One half height times sum of A plus a plus root Aa.
- D) One half height times sum of A plus a plus root Aa.
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Answer: One third height times sum of A plus a plus root Aa.
The volume of a frustum is given by V = (1/3)h(A + a + sqrt(Aa)). A common error is to use the formula for a prism or to forget the square root term involving the product of the areas.
Want to test yourself on the remaining cards for this topic?
13 more questions on Frustums & truncated solids — plus mistakes tracking and spaced repetition across the whole Maths spec.