Determine the ratio of the volume of a cube to that of the sphere

Q) Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.

Ans. Let’s draw the diagram for the given question:

Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.

If the radius of the sphere is R, then volume of the sphere, V_S = $\frac{4}{3} \pi (R)^3$

If the side of the cube is X, then volume of the Cube V_C = X³

For a sphere to be exactly fit into a cube, its Diameter has to be equal to the side of the cube

∴ X = 2R

∴ V_C = (2R)³ = 8 R³

Now $\frac{V_c}{V_s} = \frac{8 R^3}{\frac{4}{3} \pi (R)^3}$

= $\frac{(8 \times 3)}{(4\pi)} = \frac{6}{\pi}$

Therefore, the ratio of Cube’s volume to Sphere’s volume will be $\frac{6}{\pi}$

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