Pythagoras in 3D
Edexcel GCSE Maths revision on Pythagoras in 3D. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 10 practice questions on this topic.
Sample questions (3 of 10)
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Question 1
What is the length of the space diagonal in a cube with a side length of 5 centimetres?
- A) 8.66 centimetres because root 75
- B) 7.07 centimetres because root 50
- C) 5.00 centimetres because root 25
- D) 9.25 centimetres because root 85
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Answer: 8.66 centimetres because root 75
The correct answer is 8.66 centimetres because the space diagonal is calculated as 5 times the square root of 3, which is approximately 8.66. A common mistake is using the face diagonal formula instead, which leads to 7.07.
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Question 2
For a cuboid with dimensions 3 cm, 4 cm, and 12 cm, what is the length of the diagonal connecting opposite corners?
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Answer: 13
The correct answer is 13. You calculate this by finding the square root of (3 squared + 4 squared + 12 squared), which is the square root of 169.
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Question 3
Which expression represents the length of the space diagonal d of a cuboid with length l, width w, and height h?
- A) d equals square root of l2 plus w2 plus h2
- B) d equals square root of l2 plus w2 minus h2
- C) d equals square root of l plus w plus h squared
- D) d equals square root of l2 times w2 plus h2
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Answer: d equals square root of l2 plus w2 plus h2
The correct answer is d equals square root of l2 plus w2 plus h2. This formula is derived by applying Pythagoras twice: first to find the diagonal of the base, then to find the space diagonal using the height.
Want to test yourself on the remaining cards for this topic?
7 more questions on Pythagoras in 3D — plus mistakes tracking and spaced repetition across the whole Maths spec.