Question

Twenty seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S^{\prime }$. Find the radius $r^{\prime }$ of the new sphere.

• A. $3r$
• B. $4r$
• C. $5r$
• D. $2r$

Answer 1

The correct option is A $3r$

Volume of resulting sphere $=27\times$ ( Volume of one iron sphere )

Volume of a sphere $=\frac{4}{3}\pi r^3$
Let $r^{\prime }$ be the radius of the resulting sphere.
So, $\frac{4}{3}\pi {\left(r^{{}^{\prime }}\right)}^3=27\times \frac{4}{3}\pi r^3$
$=>{\left(r^{{}^{\prime }}\right)}^3=27\times r^3$
$=>r^{{}^{\prime }}=3\times r$
Hence, radius of the resulting sphere is $3r$.