Question

The volume of a sphere is $\frac{4}{3}\pi r^3$ cubic units, then the ratio of the volume of a cube to that of a sphere which will fit inside the cube is:

• A. $\frac{4}{3}:\pi$
• B. $6:\pi$
• C. $4:3$
• D. $4:\pi$

Answer 1

The correct option is B $6:\pi$

Let the side of cube is a cm

Then area of volume =$a^3$

Then radius of sphere =$\frac{a}{2}$

Then valume of sphere=$\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3=\frac{\pi a^3}{6}$

So ratio =$a^3:\frac{\pi a^3}{6}::6:\pi$