The ratio of the volume of a cube to that of a sphere which will fit inside the cube is

Let edge of cube be $$2a$$ cm and thus diameter of sphere = $$2a$$ cm

=> Radius of sphere = $$\frac{2a}{2}=a$$ cm

Volume of cube = $$(2a)^3=8a^3$$ $$cm^3$$ -----------(i)

Volume of sphere = $$\frac{4}{3}\pi r^3$$

= $$\frac{4}{3} \pi \times(a)^3=\frac{4a^3\pi}{3}$$ $$cm^3$$ -----------(ii)

Dividing equation (i) by (ii), we get :

=> Required ratio = $$\frac{8a^3}{\frac{4a^3\pi}{3}}$$

= $$\frac{8\times3}{4\pi}=\frac{6}{\pi}$$

$$\therefore$$ Ratio of the volume of a cube to that of a sphere which will fit inside the cube = $$6:\pi$$

=> Ans - (C)