Question

the minute hand of watch is 2.1 cm long. how far does the tip moves in 45 minute?​

Answer 1

Given

• Length of minute hand = 2.1cm

To Find

• $\text{How far does the tip moves in 45 minute}$

___________Solution__________

we know that

• Length = rθ

where, r is minute hand of clock = 2.1 cm

Finding Angle θ

• $\boxed{In ~~ r ~~ = \dfrac{1}{ θ} ,~~ θ~~ is~~ in~~ radian}$

We know that,

• Minute hand make 1 revolution in 1 hour

Hence we can say that,

• Minute hand completes 360 in one hour

therefore,

$\sf{Degree \: \: completed \: \: in \: \: 1 \: minute = \dfrac{360}{60} }$

$\sf{Degree \: \: completed \: \: in \: \: 45 \: minute = \dfrac{360}{60} \times 45\degree}$

$\sf{\quad \quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad= 6 \times 45\degree}$

$\sf{\quad \quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad= 270\degree}$

Hence,

${\sf~~~~~~~\implies θ = 270° }$

• ${(Radian \: \: measure \: \: = \dfrac{π}{180} \: \: Degree \: \: measure )}$

${\sf~~~~~~~ = 270° \times \dfrac{\pi}{180 \degree} }$

${\sf~~~~~~~ = \dfrac{3\pi}{2 } }$

Now putting the value in formula

${\sf ~~~~~~~\implies ~~ l= rθ}$

${\sf ~~~~~~~\implies ~~ l= 2.1 \times \dfrac{3\pi}{2} }$

${\sf ~~~~~~~\implies ~~ l= 1.05 \times 3\pi }$

${\sf ~~~~~~~\implies ~~ l=3.15 \times \pi }$

${\bf ~~~~~~~\implies ~~ l≈10cm}$

$\text{10cm far will the tip moves in 45 minute.}$

Answer 2

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