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Ex 5.5
13. The hour hand of a clock is 12cm long. Find the exact
a) length of the arc through which the hand would turn in 5 hours ( using the formula L= rФ where L=arc length and r= radius and Ф is the angle in radians.)
b) the area through which the hand would pass in 2 hours

Sagot :

konrad509
a)
[tex]r=12 \text{ cm}\\ \phi=5\text{ h}=30^{\circ}=\dfrac{30\pi}{180} \text{ rad}=\dfrac{\pi}{6} \text{ rad}\\ L=12\cdot\dfrac{\pi}{6} =2\pi \text{ cm}[/tex]

b)
[tex]A=\dfrac{\alpha \pi r^2}{360}\\ r=12 \text{ cm}\\ \alpha =2 \text{ h}=2\cdot30=60^{\circ}\\ A=\dfrac{60\cdot \pi \cdot 12^2}{360}\\ A=24\pi \text{ cm}^2[/tex]
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