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
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.