Question

The largest sphere is carved out of a cube of edge 14 cm. The volume of this sphere is:

• A. 1370 ${\text{cm}}^3$
• B. 1800 ${\text{cm}}^3$
• C. 1437 ${\text{cm}}^3$
• D. 1734 ${\text{cm}}^3$

Answer 1

Answer: (C)

1437 ${\text{cm}}^3$

The largest sphere that can be carved out of a cube will have diameter equal to length of the side of the cube.

Diameter $=14\text{cm}$

$\Rightarrow$ Radius, $r=7\text{cm}$

Volume of the sphere, $V=\frac{4}{3}\pi r^3$

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

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

$=\frac{88}{3}\times 49{\text{cm}}^3$

$=1437.33{\text{cm}}^3$