Math CentralQuandaries & Queries


Question from Danny:

How many gallons of water in a glass bowl with the dimensions of 10 inches high
and 13.5 inches wide?


Hi Danny,

By a "glass bowl" I assume the shape of the bowl is spherical as in the diagram below.


The section shaded blue is called a spherical cap and if you know some calculus you can find its volume as a volume of revolution. The volume is given by

\[V = \frac{\pi \; h^2}{3}\left( 3r - h\right)\]

where in your case $h = 10$ inches and $r = \large \frac{13.5}{2}$ inches. I got $V = 1073.38$ cubic inches. (you should check my arithmetic.)

To find the volume in gallons you could type

what is 1073.38 cubic inches in gallons

into the Google search window or, I'm a Mac user so I said

Hey Siri, what's 1073.38 cubic inches in gallons.


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