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Solution 4.1:9
From Förberedande kurs i matematik 1
\displaystyle \alpha =\frac{1}{6}\centerdot 2\pi
radians
\displaystyle =\frac{\pi }{3}
radians
The area of the sector is
Area \displaystyle =\frac{1}{2}\alpha r^{2}=\frac{1}{2}\centerdot \frac{\pi }{3}\centerdot \left( 8\ \text{cm} \right)^{2}=\frac{32\pi }{3}\ \text{cm}^{2}\approx 33.5\ \text{cm}^{2}