Geometry and TrigonometryVery hardBase side of a box from its volume
Geometry and Trigonometry practice question
A rectangular box has a square base, and its height is twice the side length of the base. The volume of the box is 128 cubic centimetres. What is the side length of the base, in centimetres?
Answer: 4
With side s, the volume is s · s · 2s = 2s³ = 128, so s³ = 64 and s = 4.
Common wrong answers
- If you answered 8
- 8 is the height (2 × 4), not the base side.
- If you answered 64
- 64 is s³, not s.
- If you answered 5.04
- 5.04 is the cube root of 128, forgetting the factor 2 in the height.
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