The largest sphere is cut off from a solid cube of side 6 cm. The volume of the sphere will be:

Correct option is C

Given:

Side length of the cube = 6 cm
Diameter of the sphere = 6 cm

Formula Used:

The volume V  of a sphere is given by the formula:

$$V = \frac{4}{3} \pi r^3$$

Solution:

The largest sphere that can fit inside a cube will have a diameter equal to the side length of the cube.

Side length of the cube = 6 cm

Diameter of the sphere = 6 cm

The radius r  of the sphere is half of its diameter:

​$$r = \frac{\text{Diameter}}{2} = \frac{6}{2} = 3 \, \text{cm}$$​

The volume V  of a sphere is given by the formula:

​$$V = \frac{4}{3} \pi r^3$$​

​$$V = \frac{4}{3} \pi (3)^3$$​

​$$V = \frac{4}{3} \pi (27)$$​

​$$V = \frac{4}{3} \times 27 \times \pi$$​

​$$V = 36 \pi \, \text{cm}^3$$

Option (C) is right.