Math CentralQuandaries & Queries


Question from Mack:

I need to find how close the actual volume was of a cylinder (with both ends closed)
to being optimized. Can you please send step by step response?

Height = 11cm
Circumference = 24.4cm


Hi Mack,

The volume $V$ of a circular cylinder is given by

\[V = \; \pi \; r^2 h\]

where $r$ is the radius of the base and $h$ is the height. You know that $h=11$ cm so all you need is the radius.

The circumference $C$ of a circle is given by

\[C = 2 \; \pi \; r\]

where again $r$ is the radius. You know that $C=24.4$ cm so substitute this into the above expression and solve for $r.$ Substitute this value of $r$ into the expression for $V.$ This will give the volume in cubic centimeters.


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