Question

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

Answer 1

a)

`r=12 \text{ cm}\\ \phi=5\text{ h}=30^(\circ)=(30\pi)/(180) \text{ rad}=(\pi)/(6) \text{ rad}\\ L=12\cdot(\pi)/(6) =2\pi \text{ cm}`

b)

`A=(\alpha \pi r^2)/(360)\\ r=12 \text{ cm}\\ \alpha =2 \text{ h}=2\cdot30=60^(\circ)\\ A=(60\cdot \pi \cdot 12^2)/(360)\\ A=24\pi \text{ cm}^2`