Chapter 8.4, Problem 59E

Area of a segment of a circle Use two approaches to show that the area of a cap (or segment) of a circle of radius r subtended by an angle θ (see figure) is given by

$A_{\text{seg}}=\frac{1}{2}{r}^2(\theta -\sin \theta ).$

1. a. Find the area using geometry (no calculus).
2. b. Find the area using calculus.