The rule of the volume of the cylinder is
[tex]V=\pi\times r^2\times h[/tex]r is its radius
h is its height
Since the vase is shaped a cylinder, with a diameter 8 in and height of 7 in, then
[tex]\begin{gathered} r=\frac{1}{2}\times8=4in. \\ h=7in\text{.} \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} V=3.14\times(4)^2\times(7) \\ V=351.68in.^2 \end{gathered}[/tex]Since the volume of the water is 2/3 the volume of the vase, then
[tex]\begin{gathered} V_w=\frac{2}{3}\times351.68 \\ V_w=234.4533333in^3 \end{gathered}[/tex]Round it to the nearest hundredth, then
[tex]V_w=234.45in^3[/tex]The volume of the water in the vase is 234.45 cubic inches
