Question

27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere. Find the radius of the big sphere formed.

• A. 3 cm
• B. 9 cm
• C. 15 cm
• D. 5 cm

Answer 1

The correct option is C

15 cm

Volume of the big iron ball will be equal to the volume of 27 small iron balls.
Let the radius of the big sphere be R cm.
Let the radius of the small sphere be
r cm = 5 cm.

$\Rightarrow \frac{4}{3}\times \pi R^3=27\times (\frac{4}{3}\times \pi r^3)$

$\Rightarrow R^3=27r^3$

$R=3r=3\times 5=15$ cm.