Question

27 spherical iron balls of radius 5 cm each are melted and recast 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 sphere will be equal to the combined volume of the 27 spherical iron balls.
Let the radius of the big sphere be R cm. Then, as per the data given:

$\frac{4}{3}\times \pi R^3=27\times (\frac{4}{3}\times \pi \times 5^3)$

$\Rightarrow R^3=3^3\times 5^3$

$\Rightarrow R=3\times 5=15$ cm