solve in detail?

Question

the length of the minute hand of a clock is 10.5cm.It's end covers a distance of 22cm while travelling from 55minutes past 12 to x mins past 1.Then x=?

Answer 1

let us assume that the minute hand has traced an angle 'a' in covering the distance.

2*pi*r*a/360 = distance covered where pi = 22/7 and r = 10.5 cm.

so a = 22*360/2*pi*r = 120 degrees


the clock has a total of 360 degrees.

so 360 degrees = 60 min.

120 min = 60/3 = 20min

so the min hand moves for twenty minutes .

so now the time is 15 min past 1

so x = 15

Answer 2

C = 21 π
r = 10.5 cm
Arc length = 22 cm

21π cm<--->360°
22 cm<-->(22/ 21π) x 360° = 120°

360°<---> 60 min
120°<---> 20 min

12:55 + 0:20 = 13:15
x = 15

Answer 3

Perimeter of a circle = 2 x pi x r

where, pi = 3.142 and r = radius

r = 10.5cm

perimeter of clock = 2 x 3.142 x 10.5 = 65.98 cm

Divide by 60 to get each minute increment distance;

65.98 / 60 = 1.0997 cm

therefore, if 22cm are covered,

22cm is equivalent to (22/1.0997) cm = 20.01 minutes (approx 20 mins)

Therefore x = 15 minutes