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Solution 4.1:9

From Förberedande kurs i matematik 1

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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
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<center> [[Bild:4_1_9_.gif]] </center>
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<center> [[Bild:4_1_9.gif]] </center>
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{{Displayed math||<math>\alpha = \frac{1}{6}\cdot 2\pi\ \text{radians} = \frac{\pi}{3}\ \text{radians.}</math>}}
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<center> [[Image:4_1_9_.gif]] </center>
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The area of the sector is
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{{Displayed math||<math>\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{.}</math>}}

Current revision

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

=612 radians=3 radians.
Image:4_1_9_.gif

The area of the sector is

Area=21r2=213(8 cm)2=332 cm233.5 cm2.
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