Two identical cylindrical pipes of radius 3 cm meet at right angles, their axes crossing at one point. The solid region common to both cylinders is known to have volume $16r^3/3$, where $r$ is the radius. Find that volume in ${\text{cm}}^3$. Take π = 3.14.

Substitute $r=3$ directly: $16\times 3^3/3=16\times 27/3=144{\text{cm}}^3$. Notice the formula carries no π at all, which is the surprise of this solid$.(113.04{\text{cm}}^3$ is (4/3)π(27), the sphere of radius 3 that sits inside the common region — the region is bigger than that sphere, and it is not a sphere; $48{\text{cm}}^3$ uses $r^2$ instead of $r^3$; $288{\text{cm}}^3$ doubles, as if the two cylinders each contributed a separate copy.)