Radian Measure Math Example 4

Solution

1. 1
   In $20$ minutes, the minute hand sweeps $\frac{20}{60}=\frac{1}{3}$ of a full rotation $= \frac{1}{3}\times2\pi=\frac{2\pi}{3}$ rad.
2. 2
   Arc length: $s=r\theta=15\times\frac{2\pi}{3}=10\pi\approx31.4$ cm. Sector area: $A=\frac{1}{2}(15)^2\cdot\frac{2\pi}{3}=\frac{1}{2}\cdot225\cdot\frac{2\pi}{3}=75\pi\approx235.6$ cm².