Frustums & truncated solids
Edexcel GCSE Maths revision on Frustums & truncated solids. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 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 formed when a plane cuts parallel to the base of a cone?
- A) A smaller circle
- B) A wider ellipse
- C) A closed square
- D) A curved sector
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Answer: A smaller circle
The correct answer is a smaller circle. When a plane cuts a cone parallel to its base, the resulting cross-section is always a circle with a radius smaller than the original base. Many students mistakenly guess an ellipse, but that only occurs if the plane is tilted.
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Question 2
How many surfaces does a frustum of a square-based pyramid possess?
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Answer: 6
A frustum of a square-based pyramid has 6 faces in total. This includes the square top, the square base, and the four identical trapezoidal sides that connect the two squares.
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Question 3
Which of these expressions represents the volume of a frustum of a cone with base radius R and top radius r?
- A) One third pi h times R squared plus Rr plus r squared
- B) One third pi h times R squared minus Rr plus r squared
- C) One third pi h times R squared plus Rr times r squared
- D) One third pi h times R squared minus Rr minus r squared
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Answer: One third pi h times R squared plus Rr plus r squared
The correct formula is one third pi h multiplied by (R^2 + Rr + r^2). The most common error is forgetting the middle term Rr, which accounts for the geometry of the transition between the two radii.
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.