Question

the minute hand of the circular clock is 11 cm long how far does the tip of the minute hand move in 2 hours take Pi 3.14​

Answer 1

Given minute hand is 11 cm long

And we know that the total angle between the initial and final position between of the minute hand at 12 is 360°

So A/Q ,we need to calculate the total distance moved by the minute hand in 2 hour so see need to calculate out first that how what is the angle between the initial position of the minute hand at 12 and at the 1 hour poisition

So fir this we need to divide the total angle by 12

$\frac{360}{12} = 30 \degree$

So fir two hour

$\theta = 30 \times 2 = 60 \degree$

So we need to calculate out the length of arc by using the formula that is

$\huge{\red{ \frac{ \theta}{360} \times \pi \: \times r ^{2} - r^{2} \times sin \frac{ \theta}{2} \times cos \frac{ \theta}{2} }}$

let us calculate out

$= > \frac{60}{360} \times 3.14 \times 121 - 121 \times sin30 \times cos30 \\ \bold{ r = 11cm \: \because \: given \: length \: of \: hand \:is \: 11cm} \\ \\ = > \frac{1}{6} \times 3.14 \times 121 - 121 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} \\ \\ = > \frac{379.9}{6} - \frac{121 \times 1.7}{4} \\ \\ \because \sqrt{3} = 1.7 \\ \\ = > \frac{379.9}{6} - \frac{205.7}{4} \\ \\ = > \bold{ we \: need \: to \: take \: LCM \: now \: } \\ \\ LCM = 12 \\ \\ = > \frac{2 \times 379.9 - 205.7 \times 3}{12} \\ \\ = > \frac{759.8 - 617.1}{12} \\ \\ = > \frac{142.7}{12} \\ \\ = > \red{\huge{distance \: moved = 11.89 \: cm}}$