The right circular cylinder above (Geometry Figure 30) has axis $PQ$. If the radius of each circular base is $r = 4$ and the length of axis $PQ$ is $7$, what is the **volume** of the cylinder?

For a right circular cylinder, the axis is perpendicular to the bases, so the length of the axis equals the height. Here $h = 7$. Volume: $V = \pi r^{2} h = \pi (4^{2})(7) = \pi (16)(7) = 112 \pi$. - Trap A ($28 \pi = \pi \cdot 4 \cdot 7$) uses $r$ rather than $r^{2}$. - Trap B ($56 \pi = 2 \pi r h$) gives the lateral surface area, not the volume. - Trap D ($196 \pi = 49 \pi \cdot 4$) confuses $r$ and $h$ in the squaring. The figure is essential because it labels the axis $PQ$ as the cylinder's principal axis — without that label you might not realise the labelled segment is the height.