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Question
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
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Solution
Let the radius of spherical ball = r
∴ Volume = `4/3pir^3`
Radius of smaller ball = `r/2`
∴ Volume of smaller ball = `4/3pi(r/2)^3`
= `4/3pir^3/8`
= `(pir^3)/6`
Therefore, number of smaller balls made out of the given ball
= `(4/3pir^3)/((pir^3)/6)`
= `4/3 xx 6`
= 8
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