🔍 Key Concepts

• Taper per foot (TPF) is usually based on the change in diameter over a known length, then converted to a 12-inch (1 foot) basis. • Be clear on what length actually has the taper: in this illustration, the dimension X marks the tapered section; the small fillet radii R at each end do not significantly change the taper length for this type of exam problem. • Use the relationship: TPF = (change in size over the taper length) × (12 inches per foot). Decide whether "size" means diameter or radius based on how E and F are labeled.

💭 Think About

• Are the given values E = 2.5" and F = 6" shown as diameters of cylindrical sections at each end of the taper, or as radii? How does that affect the "change in size" you should use? • Which dimension on the drawing actually corresponds to the length over which the diameter changes from E to F? Is it the entire shaft length (42"), or just X (8")? • Once you know the change in diameter and the taper length, how do you scale that change so it represents how much the diameter changes over 12 inches instead of over 8 inches?

✅ Before You Answer

• Confirm from the illustration that E and F are diameters, not radii, before using them in the formula. • Make sure you use X = 8 inches as the taper length, not the 42-inch overall shaft length. • After you compute the TPF numerically, compare your result to the choices and check which option is closest to your calculated taper per foot.