A lead ball of radius 6 cm is melted down and re-cast into ball bearings of radius 1.5 cm. How many ball bearings can be produced?TOPIC- Similarity:VOlume and surface area of similar solids

1 Answer

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tiburtius | High School Teacher | (Level 2) Educator

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Volume of ball is `V=4/3 r^3 pi.` So for the big ball we get

`V=4/3 6^3 pi`

and for `n` smaller balls we have

`V=n 4/3 1.5^3 pi`

Those two volumes must be equal bacause `n` smaller balls are made of the bigger ball.

`4/3 6^3 pi = n 4/3 1.5^3 pi`

Now we multiply whole equation with `3/(4 pi)`

`1.5^3 n = 6^3` `Rightarrow n=(6^3)/(1.5^3)`


You can make 64 ball bearings of 1.5 cm radius from one ball of 6 cm radius.