id: 06150405
dt: j
an: 2013b.00588
au: Pritchard, Chris
ti: Ball in a box.
so: Math. Sch. (Leicester) 41, No. 1, 25-27 (2012).
py: 2012
pu: Mathematical Association (MA), Leicester
la: EN
cc: G30 I40
ut: solid geometry; volume; spheres; cubes; cylinders; cones; ratio;
optimization; differentiation
ci:
li:
ab: Summary: The article presents pairings of 2-dimensional (2-D) shapes
occupying space inside other shapes to 3-dimensional (3-D) analogues.
It provides the formula to obtain the proportion of volume of a cube
occupied by a sphere in a cube. It cites the formula to obtain the
volume of a sphere occupied a cube in a sphere. It notes formulas to
obtain the ratio of the volumes of cylinders in a cube and similar
scenarios.
rv: