ANSWER:
392.5 in^3
STEP-BY-STEP EXPLANATION:
We must calculate the volume of the bottle and then divide it by 2 to find the answer.
We know that the volume of a cylinder is:
[tex]V=\pi\cdot r^2\cdot h[/tex]The radius is half the diameter therefore we calculate it and replace it in the formula like this:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{10}{2}=5 \\ \text{replacing } \\ V=3.14\cdot5^2\cdot10 \\ V=785 \end{gathered}[/tex]Now we divide by two to calculate the volume in half (1/2)
[tex]\begin{gathered} V=\frac{785}{2} \\ V=392.5 \end{gathered}[/tex]