Recall the formula for the volume of a cylinder.

$\text{Cylindrical volume}=(\text{area of the base})\times(\text{height})$

Divide the octagonal base into congruent triangles to find its area.

Now use the formula $(\text{volume})=(\text{area of the base})\times(\text{height})$ to find the volume of the prism.

$\text{Base Area}\approx19.3\text{ units}^2$
$\text{Volume}\approx(19.3)(7)\approx135.2\text{ units}^3$