[tex]\begin{gathered} \text{cylinder's volume=}\pi r^2h \\ r=6\operatorname{cm} \\ h=10cm \\ \pi\approx3.14 \\ \text{cylinder's volume=(3.14)}(6)^2(10) \\ \text{cylinder's volume=}1130.4cm^3 \\ Shelly\text{ has to fill her glass with a half of its volume, hence} \\ \text{volume=}\frac{1130.4cm^3}{2} \\ \text{volume=565.2}cm^3 \\ Shelly\text{ has to fill her glass with 565.2}cm^3\text{ of water} \end{gathered}[/tex]
