Pythagoras in 3D
AQA GCSE Maths revision on Pythagoras in 3D. 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
A student is asked to find the length of the space diagonal of a cuboid. They calculate the diagonal of the base, then use that result as one side in a second right-angled triangle. What is the name of the theorem they are applying twice?
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Answer: Pythagoras' theorem
Finding a 3D diagonal requires finding a 2D diagonal on the floor first. You then use that 2D diagonal and the vertical height to form a second right-angled triangle, applying Pythagoras' theorem again to find the space diagonal.
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Question 2
Which of the following is a necessary condition to use Pythagoras' theorem in a 3D shape problem?
- A) The shape must be a regular tetrahedron
- B) The triangle used must contain a right angle
- C) The shape must have exactly six faces
- D) All sides of the shape must be equal
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Answer: The triangle used must contain a right angle
Even within a complex 3D shape, you must identify a triangle where two sides meet at 90 degrees. Without this right angle, the relationship a squared plus b squared equals c squared does not hold true.
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Question 3
When calculating the space diagonal of a cuboid with dimensions length, width and height, why is the square root only applied at the very end of the calculation?
- A) To avoid rounding errors early in the process
- B) Because the formula requires the sum of the dimensions
- C) To ensure the units remain squared
- D) Because the diagonal is shorter than the sum of the sides
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Answer: To avoid rounding errors early in the process
If you round the length of the base diagonal before squaring it for the next step, the error is magnified. Keeping the value as a square root or an unrounded decimal until the final step maintains precision.
Want to test yourself on the remaining cards for this topic?
13 more questions on Pythagoras in 3D — plus mistakes tracking and spaced repetition across the whole Maths spec.