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(in cm).

• A. 12
• B. 21
• C. 18
• D. 15

Answer 1

The correct option is A

12

Radius of first sphere $=r_1=6cm$
Radius of second sphere $=r_2=8cm$
Radius of third sphere $=r_3=10cm$
Let radius of resulting sphere be $rcm$.
According to given condition, we have
Volume of first sphere + Volume of second sphere + Volume of third sphere = Volume of resulting sphere
$\Rightarrow \frac{4}{3}\pi (r_1{)}^3+\frac{4}{3}\pi (r_2{)}^3+\frac{4}{3}\pi (r_3{)}^3=\frac{4}{3}\pi r^3$

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

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

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

$\Rightarrow r^3=1728$

$\Rightarrow r=12cm$