Question

A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find tbe number of balls.

Answer 1

Let the radius of sphere be R

Let the radius of spherical balls be r

volume of sphere=(volume of spherical balls )n

4÷3πR3=(4÷3πr 3)n

R3=(r3)n

3×3×3=(0.3×0.3×0.3)n

27. =(0.27)n

n=100

113.14=(11.31)n

Answer 2

Let the number of balls be n

Diameter of small spherical balls = 0.6 cm

So, Radius of small spherical balls = 0.6/2 = 0.3 cm

Now, the Radius of solid sphere = 3 cm

Now, the volume of small spherical balls = 4/3πr^3

= 4/3*22/7*0.3*0.3*0.3

Now the volume of solid sphere = 4/3πr^3

=4/3*22/7*3*3*3

We know that the n = volume of solid ball/volume of small ball

Therefore, n = (4/3*22/7*3*3*3) / (4/3*22/7*0.3*0.3*0.3)

n = 3*3*3/0.3*0.3*0.3

n = 27/0.027

n = 1000

Hope the answer is helpful !!

Good Day !!