Question

A sphere with radius 12 cm is melted into 27 smaller spheres with equal radius. Find the radius of smaller spheres

Answer 1

Answer:

4 cm

Step-by-step explanation:

Write R for the radius of the original sphere.  So R = 12 cm.

Let V be the volume of the original sphere.  So V = 4 π R³ / 3.

Let v be the volume of one of the small spheres.

So v = V / 27 =  ( 4 π R³ / 3 ) / 27

Let r be the radius of one of the small spheres.

So v = 4 π r³ / 3.

Equating the two expressions for v, we have

4 π r³ / 3 = ( 4 π R³ / 3 ) / 27

=>  r³ = R³ / 27   ( cancel 4 π / 3 )

=> r = R / 3     ( take cubed root )

=> r = 12 cm / 3 = 4 cm.