Question

If a solid metallic sphere of radius 16 cm is melted and recast into m spherical solid balls of radius 2 cm then the value of m is equal to ???

Answer 1

hllo frnd ur answer is as follows....✌✌

Radius of the sphere r=16cm
volume v =4/3πr³
v=4x22x(16)³/3x7
v=360448/21
v=1764.19cm³
This sphere is recast into m spheres of radius =2cm
volume of m spheres V=m4/3πr³
V=m4x22x(2)³/3x7
V=m704/21

V=m33.52cm³
The volume of the solid sphere must be equal to the Spheres that has been recasted.
m33.52=1764.19
m=1764.19/33.52
m=512(approx).
This is the required answer. 
#arjun

Answer 2

Here in case of recasting the volume of the total material will remain same.

So we can write,
Volume of the original big sphere= m x volume of single small sphere

Now, Volume of a sphere is given by V=(4/3)πr³
Volume of bigger sphere
=(4/3)π(16)³
= 4096 x (4/3)π

Volume of one small sphere
=(4/3)π(2)³
=8 x (4/3)π

Now according to conservation of volume
4096 x (4/3)π = m x [8 x (4/3)π]
So, m=4096/8
m=512

so there will be 512 new small spheres after recasting.