Question

A solid sphere of radius 3 cm is melted and then casted into small spherical balls each of diameter 0.6cm. find the radius of balls thus obtained​

Answer 1

Answer:

1000 spherical balls of radius 0.3cm will be obtained.

Step-by-step explanation:

Given the radius of the sphere = 3cm = R

This sphere is melted and recasted into new small spheres having the diameter = 0.6 cm

=> radius of the small sphere = r = 0.3cm   (as Radius = Diameter/2)

We know that during the recasting procedure, the volume of the shapes remain the same.

=> Volume of the big sphere = Volume of the small spheres * No. of spheres

Let the number of spherical balls be formed be n

We know that Volume of a sphere = (4/3) π r³

=>  (4/3) π R³ =  (4/3) π r³ * n

Substituting the values from above,

=>  (4/3) π (3)³ =  (4/3) π (0.3)³ * n

=> (3)³ = (0.3)³n

=> 1000 = n

Therefore, 1000 spherical balls of radius 0.3cm will be obtained.