SOLUTION: A Solid sphere of radius 3cm is melted and then cast into small spherical balls each of diameter 0.6cm. Find number of balls thus obtained.

Question 258342: A Solid sphere of radius 3cm is melted and then cast into small spherical balls each of diameter 0.6cm. Find number of balls thus obtained.
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
pi*r^3=volume of sphere
pi*27 =volume of larger sphere
pi*r^3
pi*.6^3
27/.6^3=125 balls
another way is
3/.6=5
5^3=125

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
volume of sphere is 4/3 * pi * r^3.

r = 3 cm

volume of sphere is 4/3 * pi * (3)^3 = 4/3 * 27 * pi = 4*9 * pi = 36 * pi cubic cm.

each small spherical ball has a diameter of .6 cm.

this means that each small spherical ball has a radius of .3 cm because radius = diameter / 2.

volume of each small spherical ball is equal to 4/3 * pi * r^2.

since r = .3, then volume of each small spherical ball is equal to 4/3 * pi * (.3)^3 = 4/3 * pi * .027 = .036 * pi cubic cm.

divide 36 * pi by .036 * pi and you get:

36 * pi / .036 * pi = 36 / .036 = 1000

you can make 1000 small spherical balls out of the one big spherical ball.

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