Question

27 spherical iron balls of radius 7 cm each are melted and recasted into a big sphere. Find the radius of the big sphere formed.

• A. 11 cm
• B. 21 cm
• C. 20 cm
• D. 10 cm

Answer 1

The correct option is B 21 cm

Volume of the big iron ball is equal to the volume of 27 small iron balls.
Let the radius of the big sphere be
R cm and the radius of the small sphere be r cm.
Given, r = 7 cm

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

$\Rightarrow R^3=27r^3$
$\Rightarrow R=3r$
$\Rightarrow R=3\times 7$
$\therefore$ The radius of the big sphere is $R=21$ cm