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Question

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?


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Solution

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.


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