Question

Twenty-seven solid iron spheres, each of radius r and surface area s are melted to form a sphere with surface area s'. The radius (r) of the new sphere k is

• A. 5
• B. 4
• C. 3
• D. $\frac{5}{3}$

Answer 1

The correct option is C 3

Volume of 27 solid sphere, each of radius, $r=27\times \frac{4}{3}\pi r^3=36\pi r^3$
According to the statement,
Volume of sphere of radius r’ = Volume of 27 solids spheres
$\Rightarrow \frac{4}{3}\pi (r^{\prime }{)}^3=36\pi r^3$
$\Rightarrow (r^{\prime }{)}^3=27r^3=(3r{)}^3\Rightarrow r^{\prime }=3r$