A cuboid whose base is a square of side $4$ inches, and height $6$ inches is placed in a cylinder.
Cylinder has a radius of $2\sqrt{2}$ inches, and height $6$ inches. The gap between cuboid and cylinder is filled with $n$ spheres of radius $0.4$ inches. What can be the maximum value of $n$?
I can figure out that the unoccupied volume will be $48\pi – 96$
and the gap between cylinder and sphere is of approx $0.8$ inches, which means one sphere can be fit in. But how to figure out how many spheres can be there?
Best Answer
I'm showing below how to arrange 14 spheres into each gap. Computing $x$ and $y$ via Pythagoras' theorem is not difficult: $$ (2+0.4)^2+x^2=(2\sqrt2-0.4)^2,\quad (2x)^2+y^2=0.8^2. $$ You may check that $y\le0.4$.