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To find the volume of a cylinder, Shelly needs to know the height of the cylinder. The formula for the volume \( V \) of a cylinder is:
\[
V = \text{Base Area} \times \text{Height}
\]
Since she already knows the area of the base, the missing piece of information required to calculate the volume is the height of the cylinder.
So, the correct response is:
**the height of the cylinder**