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# A water bottle in the shape of a cylinder has a volume of 500 cubic centimeters. The diameter of a base is 7.5 centimeters. What is the height of the bottle? Justify your answer.

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\begin{align*} \\ \newline \text{Volume of cylinder} &= 500 \hspace{0.1cm} \text{cm}^{3} \\ \newline \pi r^{2}h &= 500 \hspace{2 cm} (\text{Volume of cylinder = } \pi r^{2}h) \\ \newline \pi (\dfrac{7.5}{2})^{2} \cdot h &= 500 \\ \newline h &= \dfrac{500}{\dfrac{225\pi}{16}} \hspace{2.5 cm} \text{(Re-arranging)} \\ \newline h &= 11.3 \hspace{0.1cm} \text{cm} \\ \end{align*}

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