Question

The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.

• A. $606.375c{m}^3$
• B. $66.3c{m}^3$
• C. $60.375c{m}^3$
• D. $66.375c{m}^3$

Answer 1

The correct option is A $606.375c{m}^3$

We have,

Diameter of the largest sphere$=10.5cm\Rightarrow 2r=10.5cm\Rightarrow r=5.25cm$

$\therefore$ Volume of the sphere$=\frac{4}{3}\times \frac{22}{7}\times {\left(5.25\right)}^{3}c{m}^3$

$=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{21}{4}\right)}^{3}c{m}^3=4\times 22\times \frac{{21}^2}{64}c{m}^3$

$=\frac{11\times 441}{8}c{m}^3=606.375c{m}^3$