From Förberedande kurs i matematik 1

\displaystyle \text{1}0 seconds corresponds to \displaystyle \frac{1}{6} minutes, so that during that time period, the second hand sweeps over \displaystyle \frac{1}{6} of a turn, i.e. the sector of a circle with angle

\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}