Paul wants to put 1200 steel ball bearings (which are spherical in shape) with a radius of 5 mm, into a cylindrical container which is 30 cm high and 18 cm in diameter. Will all the bearings fit into the container?
We are going to work in cm so firrt we change
5 mm → 0.5 cm = 12cm
Each ball bearing has volume = 4/3 π(r)3
= 4/3 π(12)3
= π/6
= 0.52 cm3
Cylinder has volume = πr2h
= π(90)2(30)
Now 1200 bearings will have volume 1200 × π/6=200π=628.32cm3
So, they will be able to fit in with lots of room to spare.