Question

Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is ___.

Answer 1

Radius of the first sphere = $r_1=6cm$

Radius of the second sphere = $r_2=8cm$

Radius of the third sphere = $r_3=10cm$
Let radius of resulting sphere = r cm
According to given condition, we have
Volume of 1st sphere + Volume of 2nd sphere + Volume of 3rd sphere = Volume of resulting sphere
$\Rightarrow \frac{4}{3}.\pi .(r_1{)}^3+\frac{4}{3}.\pi .(r_2{)}^3+\frac{4}{3}.\pi .(r_3{)}^3=\frac{4}{3}.\pi .r^3$

$\Rightarrow \frac{4}{3}\left(\right(r_1{)}^3+(r_2{)}^3+(r_3{)}^3)=\frac{4}{3}.r^3$

$\Rightarrow$ $(6^3+8^3+(10{)}^3)=r^3$

$\Rightarrow$ ( 216 + 512 + 1000 ) = $r^3$

$\Rightarrow$ $r^3$ = 1728

$\Rightarrow$ r = 12 cm