Geometry and TrigonometryMediumPacking 2-centimetre cubes
Geometry and Trigonometry practice question
A crate measures 6 cm by 8 cm by 10 cm on the inside. Cubes with edges of 2 cm are packed into the crate with no gaps. How many cubes does the crate hold?
Answer: 60
Along each edge: 6/2 = 3, 8/2 = 4 and 10/2 = 5 cubes. Total: 3 × 4 × 5 = 60. (Equivalently, 480 cm³ of crate divided by 8 cm³ per cube.)
Common wrong answers
- If you answered 120
- 120 divides by 4; a 2-cm cube has volume 2 × 2 × 2 = 8.
- If you answered 240
- 240 divides 480 by 2 instead of by 2³ = 8.
- If you answered 480
- 480 is the crate's volume in cm³; each cube takes 8 cm³, so divide by 8.
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