Question

$27$ spherical iron balls of radius $5cm$ each are melted and recasted into a big sphere.The radius of the single sphere is______.

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

Answer 1

The correct option is C

15 cm

Volume of single iron ball is same as the sum of $27$ iron balls.

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

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

$\Rightarrow R=3r=15cm$