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?

Answer 1

We are going to work in cm so firrt we change

5 mm $\to$ 0.5 cm = $\frac{1}{2}cm$

Each ball bearing has volume = 4/3 $\pi (r{)}^3$

= 4/3 $\pi (\frac{1}{2}{)}^3$

= $\pi /6$

= 0.52 $c{m}^3$
Cylinder has volume = $\pi r^{2}h$

= $\pi \left(90{)}^2\right(30)$
Now 1200 bearings will have volume 1200 × $\pi /6=200\pi =628.32c{m}^3$

So, they will be able to fit in with lots of room to spare.