1 Answer

Fraser Dale · Answer 1 · 2019-03-18T00:50:48+0000

A cylinder that circumscribers a hemisphere will share a base with the hemisphere. If the base has radius
, then the volume of the hemisphere is

$V_(\rm hemisphere)=\frac12\left(\frac43\pi r^3\right)=\frac23\pi r^3$

A cylinder with radius
and height
has volume
$\pi r^3h$ , but a cylinder that circumscribes a hemisphere will have a height equal to the radius of the hemisphere, so
h=r . Such a cylinder would have a volume of

$V_(\rm cylinder)=\pi r^3$

So, the volume of the hemisphere is
$\frac23$ of the volume of the cylinder.

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