(Q11).Three metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.

Answer:

Given : Radii of the three spheres r1 = 6 cm r2 = 8 cm r3 = 10 cm

These three are melted to form a single sphere.

Let the radius of the resulting sphere be ‘r’.

Then volume of the resultant sphere = sum of the volumes of the three small spheres.

4
3
 πr3 =
4
3
 πr13 +
4
3
 πr23 +
4
3
 πr33
4
3
 πr3 =
4
3
 π ( r13 + r23 + r33 )

r3 = r13 + r23 + r33

  = ( )3 + ( )3 + ( )3

  = + +

r3 =

= × ×

r3 = ( )3

r =

Thus the radius of the resultant sphere = cm