Multiple choice

A sphere of radius $r$, inside a cube touches each one of the six sides of the cube. What is the volume of the cube in terms of $r$ ?

  1. $8r^3$
  2. $2r^3$
  3. $4r^3$
  4. $\cfrac{4}{3}\pi r^3$
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A Correct answer
Explanation

If a sphere of radius r is inside a cube and touches all sides, the side length of the cube is equal to the diameter of the sphere, which is 2r. Volume of the cube = (side)^3 = (2r)^3 = 8r^3.

AI explanation

If a sphere of radius r touches all six sides of a cube, the diameter of the sphere equals the length of the cube's side. Therefore, the side length of the cube is 2r. The volume of a cube is found by cubing the side length, giving V = (2r)^3 = 8r^3.

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