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Question
A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?
Solution
Let radius of spherical ball = r
Then radius of smaller spherical ball `=r/4`
Let n be the no. of balls made by big spherical ball.
Clearly,
Volume of big spherical balls = n × volume of one smaller ball
`4/3 pir^3 = n xx 4/3 pi (r / 4)^3`
`r^3 = n xx r^3/64`
` n = 64`
Hence, the no. of balls = 64.
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