Question

The largest sphere is carved out of a cube whose edge is of length $l$ units. Find the volume of the sphere.

• A. $\frac{5\pi l^3}{6}$
• B. $\frac{3\pi l^3}{5}$
• C. $\frac{\pi l^3}{6}$
• D. $\frac{2\pi l^3}{7}$

Answer 1

The correct option is C $\frac{\pi l^3}{6}$

The largest sphere carved out will have the diameter equal to the side of the cube.
Hence, diameter of the sphere $=l$ units
=> Radius of the sphere $=\frac{l}{2}$
Volume of a sphere $=\frac{4}{3}\pi r^3$
Hence, volume of this sphere $=\frac{4}{3}\times \pi \times {\left(\frac{l}{2}\right)}^3=\frac{\pi l^3}{6}$