Question

Metallic spheres of radii $6$ $cm$ , $8$ $cm$ and $10$ $cm$ , respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Answer 1

Let the radius if the resulting sphere be 'r' cm.
(i) Volume of 3 spheres having radii 8 cm and 10 cm.
$=\frac{4}{3}\pi (6{)}^3+\frac{4}{3}\pi (8{)}^3+\frac{4}{3}\pi (10{)}^3$
$=\frac{4}{3}\times \frac{22}{7}\left\{\right(6{)}^3+(8{)}^3+(10{)}^3\}$
$=\frac{4}{3}\times \frac{22}{7}\{216+512+1000\}$
$=\frac{4}{3}\times \frac{22}{7}\times 1728$
$=7241.14c{m}^3$
(ii) Volume of the resulting sphere, V
$=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times r^3$
$=\frac{88}{21}\times r^3$
$=4.19r^{3}c{m}^3$
$\therefore$ Volume of the resulting sphere = Volume of three spheres
$4.19r^3=7241.14$
$\therefore r^3=\frac{7241.14}{4.19}$
$r^3=\frac{724114}{419}$
$r^3=1728$
$\therefore r=12cm$
$\therefore$ Radius of the resulting sphere is 12 cm.