Question

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. (Use $\mathrm{\pi }=\frac{22}{7}$). [CBSE 2014]

Answer 1

The radius of the largest possible sphere is carved out of a wooden solid cube is equal to the half of the side of the cube.
Radius of the sphere = $\frac{7}{2}=3.5$
Volume of the wood left = Volume of cube − Volume of sphere
$$\begin{gathered} ={\left(\mathrm{Side}\right)}^3-\frac{4}{3}\mathrm{\pi }{r}^3 \\ =7^3-\frac{4}{3}\times \frac{22}{7}\times {\left(3.5\right)}^3 \\ =343-179.67 \\ =163.33{\mathrm{cm}}^3 \end{gathered}$$