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Question
in the formula $v = pi\times r^{2}\times h$, $r^{2}$ stands for.
In the volume formula for a cylinder $V=\pi\times r^{2}\times h$, $r$ is the radius of the circular - base. Squaring the radius ($r^{2}$) is part of calculating the area of the circular base. The area of a circle is given by $A = \pi r^{2}$, and multiplying by the height $h$ gives the volume of the cylinder. So $r^{2}$ is related to the area of the circular base of the cylinder.
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The area of the circular base of the cylinder divided by $\pi$ (since $A=\pi r^{2}$, so $r^{2}=\frac{A}{\pi}$)