Chapter 12.3, Problem 16E

Often, a machinist must cut a keyway in a shaft. The total depth of cut equals the keyway depth plus the height of a circular segment. The height of a circular segment is found by applying the Pythagorean theorem or by using the formula

$h=r-\sqrt{r^2-{\left(\frac{1}{2}\right)}^2}$ where h is the height of the segment, r is the radius of the shaft, and l is the length of the chord (or the width of the keyway). Find the total depth of cut shown in Illustration 4.

ILLUSTRATION 4