Question

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

• A. $163.3c{m}^3$
• B. $164c{m}^3$
• C. $165c{m}^3$
• D. $170c{m}^3$

Answer 1

The correct option is A $163.3c{m}^3$

For such sphere its diameter should be equal to the side of sphere.

Diameter of sphere $=7$ cm

So, radius $=3.5$ cm

Volume of the sphere carved out $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \frac{22}{7}\times {3.5}^3$

$=179.7c{m}^3$

${\text{Volume of the cube of edge}}^{\prime }{a}^{\prime }\text{units}=a^3=7^3=343$

$\text{Volume of the wooden left}=343–179.7=163.3c{m}^3$