Question

The largest sphere is cut off from a cube of side $5cm$. The volume of the sphere will be

• A. $27\pi {cm}^3$
• B. $30\pi {cm}^3$
• C. $108\pi {cm}^3$
• D. $\frac{125\pi }{6}{cm}^3$

Answer 1

The correct option is D $\frac{125\pi }{6}{cm}^3$

The largest sphere carved out will have the diameter equal to side of the cube.
Hence, diameter of the sphere $=5cm$
$\therefore$ Radius of the sphere $=\frac{5}{2}cm$
Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
Hence, volume of this sphere $=\frac{4}{3}\times \pi \times {\left(\frac{5}{2}\right)}^3=\frac{125\pi }{6}{cm}^3$