The largest sphere is carved out of a cube of side 7cm. Find the volume of the sphere.

Hint: Here radius of sphere is given, we have to find the volume of sphere using the formula.

Complete step-by-step answer:

The diameter of the largest sphere which can be carved out of a cube of side 7cm is 7cm
Radius of the sphere = r = $\dfrac{7}{2}cm$
Hence volume of the sphere = $\dfrac{4}{3}\pi {r^3}$
Volume of the sphere = $\dfrac{4}{3} \times \left( {\dfrac{{22}}{7}} \right) \times {\left( {\dfrac{7}{2}} \right)^3}c{m^3}$
               = $\dfrac{4}{3} \times \left( {\dfrac{{22}}{7}} \right) \times \left( {\dfrac{{343}}{8}} \right)c{m^3}$
               = \[179.66c{m^3}\]

Note: In these types of questions first think carefully about the figures inside and outside and from the question we have to get maximum or minimum according to that apply the conditions of geometry and then apply formula to get the desired result.