\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2013b.00588}
\itemau{Pritchard, Chris}
\itemti{Ball in a box.}
\itemso{Math. Sch. (Leicester) 41, No. 1, 25-27 (2012).}
\itemab
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.
\itemrv{~}
\itemcc{G30 I40}
\itemut{solid geometry; volume; spheres; cubes; cylinders; cones; ratio; optimization; differentiation}
\itemli{}
\end