Geometry and TrigonometryHardCube around a sphere
Geometry and Trigonometry practice question
A sphere of radius 3 fits exactly inside a cube, touching all six faces. What is the volume of the cube?
Answer: 216
The sphere's diameter, 6, equals the cube's edge. Volume: 6³ = 216.
Common wrong answers
- If you answered 27
- 27 is 3³, using the radius as the edge; the edge equals the DIAMETER.
- If you answered 36
- 36 is 6², a face's area, not the volume.
- If you answered 113
- 113 is about the SPHERE's volume ((4/3)π × 27); the question asks for the cube.
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