confused on to leave in centimeters or convert to cubic centimeters

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The volume $V$ of the cylinder is $65\pi \mathrm{cm}^3$. The height of the cylinder is $5$ centimeters. Use the formula $V = Bh$ to find the area of the base of the cylinder.

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Neither. An area is always square centimeters. You need to respect dimensional homogeneity, so if you divide a volume (cm^3) by a length (cm) you have an area (cm^2)

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$B$ is measured in $\mathrm{cm}^2$, $h$ - in $\mathrm{cm}$, and $V = B \times h$ in $\mathrm{cm}^2 \times \mathrm{cm} = \mathrm{cm}^3$...