Lösung 4.1:9
Aus Online Mathematik Brückenkurs 1
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Version vom 14:49, 22. Okt. 2008
10 seconds corresponds to 1/6 minutes, so that during that time period, the second hand sweeps over 1/6 of a turn, i.e. the sector of a circle with angle
| \displaystyle \alpha = \frac{1}{6}\cdot 2\pi\ \text{radians} = \frac{\pi}{3}\ \text{radians.} |
The area of the sector is
| \displaystyle \text{Area} = \frac{1}{2}\alpha r^{2} = \frac{1}{2}\cdot \frac{\pi}{3}\cdot (8\ \text{cm})^2 = \frac{32\pi}{3}\ \text{cm}^{2} \approx 33\textrm{.}5\ \text{cm}^{2}\,\textrm{.} |
