Geometry and TrigonometryHardVolume of a hollow box's walls
Geometry and Trigonometry practice question
A closed wooden box has outer dimensions 10 cm by 10 cm by 10 cm and walls 1 cm thick on every side. What is the volume of the wood, in cubic centimetres?
- A. 488Correct
- B. 512
- C. 1000
- D. 271
Answer: A. 488
Outer volume 10³ = 1000. Inner cavity: each dimension loses 2 cm (1 cm per side), so 8³ = 512. Wood: 1000 − 512 = 488.
Why the other answers are wrong
- B. 512
- 512 is the volume of the CAVITY.
- C. 1000
- 1000 is the whole outer box, cavity included.
- D. 271
- 271 uses an inner cube of side 9 (1000 − 729), subtracting the thickness once instead of twice.
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