If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is
Question
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is
Solution
The volume of a cube is given by the formula V = s^3, where s is the length of a side of the cube.
The volume of a sphere is given by the formula V = 4/3 * π * r^3, where r is the radius of the sphere.
If a sphere is inscribed in a cube, then the diameter of the sphere is equal to the side length of the cube. Therefore, the radius of the sphere is half the side length of the cube, or r = s/2.
Substituting r = s/2 into the volume formula for a sphere gives V = 4/3 * π * (s/2)^3 = π/6 * s^3.
The ratio of the volume of the cube to the volume of the sphere is therefore (s^3) / (π/6 * s^3) = 6/π.
So, the ratio of the volume of the cube to the volume of the sphere is 6/π.
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