Question

46. The minute hand of a circular clock is
14 cm long and that of hour hand is 7 cm.
Find how far does the tip of the minute and
hour hand move in 30 minutes?​

Answer 1

Answer:

distance traveled by tip of the minute hand = 44cm

distance traveled by tip of the hour hand = 1.83 cm

Step-by-step explanation:

length of the minute hand = radius of the circle swept by it

=> radius, r = 14cm

the distance traveled by its tip is given (in time) = 30min

=> angle swept by the minute hand = $\frac{30}{60}$* 360° = 30*6° = 180°

=> D, the central angle = 180°

we can say that, distance traveled by tip of the minute hand is the arc length of the sector so formed by the movement of the tip

hence, the arc length of the sector so formed = $\frac{D}{360}$*2$\pi$r units

                                                                   = $\frac{180}{360}$*2*$\frac{22}{7}$*14cm

                                                                   =   $\frac{1}{2}$*2*$\frac{22}{1}$*2 cm

                                                                   =   22 *  2 cm

                                                                   = 44 cm (distance traveled by tip of the minute hand)

distance traveled by tip of the minute hand = 44cm

similarly,

length of the hour hand = radius of the circle swept by it

=> radius, r = 7cm

the distance traveled by its tip is given (in time) = 30min = $\frac{1}{2}$hour

=> angle swept by the hour hand = $\frac{\frac{1}{2} }{12}$* 360° = $\frac{1}{24}$* 360° = 15°

=> D, the central angle = 15°

we can say that, distance traveled by tip of the hour hand is the arc length of the sector so formed by the movement of its tip

hence, the arc length of the sector so formed = $\frac{D}{360}$*2$\pi$r units

                                                                   = $\frac{15}{360}$*2*$\frac{22}{7}$*7cm

                                                                   =   $\frac{1}{24}$*2*$\frac{22}{1}$*1 cm

                                                                   =   $\frac{1}{12}$*22 cm

                                                                   = $\frac{11}{6}$ cm  or 1.83cm(distance traveled by tip of the hour hand)

distance traveled by tip of the hour hand = 1.83 cm