Question

Metallic spheres of radii 12cm, 8cm and 10cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

• A. 12
• B. 14.8
• C. 18.5
• D. 15.7

Answer 1

The correct option is B

14.8

Radius of first Sphere = $r_1=12cm$

Radius of second Sphere = $r_2=8cm$

Radius of 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
$\Rightarrow \frac{4}{3}.\pi .(r_1{)}^3+\frac{4}{3}.\pi .(r_2{)}^3+\frac{4}{3}.\pi .(r_3{)}^3=\frac{4}{3}.\pi .r^3$

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

$\Rightarrow$ $({12}^3+8^3+(10{)}^3)=r^3$

$\Rightarrow$ ( 1728 + 512 + 1000 ) = $r^3$

$\Rightarrow$ $r^3$ = 3240

$\Rightarrow$ r = 14.8 cm