A solid sphere of radius 3cm is melted and then cast into balls each of radius 0.3cm. Find the no. of balls thus obtained.
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Answer:
Let the total number of balls be x.
Volume of the solid sphere
=
3
4
πr
3
=
3
4
π×3
3
cm
3
=36πcm
3
Radius of spherical ball =
2
0.6
cm=0.3cm
Volume of a spherical ball
=
3
4
π×(0.3)
3
cm
3
=
3
4
π×
10
3
×
10
3
×
10
3
cm
3
=
1000
36π
cm
3
∴ Volume of x spherical balls
=
1000
36π
xcm
3
Clearly,
Volume of the solid sphere = Volume of x spherical balls.
⇒36π=
1000
36π
x⇒x=1000.
Hence, 1000 spherical balls are obtained by melting the given solid sphere .
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