Question

The minute hand of a clock is 2.1 cm long how far does its tip move in 20minutes use (pi =22/7)

Answer 1

Answer:

Tip covered 4.4 cm

Explanation:

How far does minute hand tip move in 20 minutes?

In 60 minute tip of minute hand make a complete circle.

$60\text{ minutes}=2\pi$

Now we find how much radian move in 20 minutes.

$1\text{ minutes}=\frac{\pi}{30}$

$20\text{ minutes}=20\times \frac{\pi}{30}\Rightarrow \frac{2\pi}{3}$

Length of minute had clock (r) = 2.1 cm

$\theta=\frac{2\pi}{3}$

Distance covered by tip of minute hand is l.

Formula: $\theta=\frac{l}{r}$

$\frac{2\pi}{3}=\frac{l}{2.1}$

$l=\frac{2\pi}{3}\times 2.1\Rightarrow 4.4\text{ cm}$     $\because \pi=\frac{22}{7}$  

Tip covered 4.4 cm

Answer 2

Hint:

As we know that the tip of the minute hand makes a complete circle when 60 minutes get completed. When the circle completes one round then it is of 2π  degrees. After this, we will convert the degrees into radians for 1 minute and we need to calculate for 20 minutes so, we will multiply the converted from by 20. Next, we will use the formula θ $=\frac{l}{r}$   and keep it equal to the expression we have found and we will evaluate the value of l.

Where,

'l' is Arc Length of the circle

'r' is Radius of the circle

'θ' is the angle formed between two Radius

Complete step by step solution:

Consider the length of the minute hand of a clock that is 2.1 cm.  

First, we will calculate the distance the minute hand moves in 20 minutes.

We know that when 60 minutes get completed implies that the tip of a minute hand makes a complete circle.

And when the circle makes one round implies that the circle is of 2π  degrees.

Thus, we get that,

          $2\pi =60\\\pi =30$

Now, we will find how much radian move in 20 minutes.

Since 1 minute equals to  $\frac{\pi }{30}$   in radians

Therefore, we will calculate the radian for 20 minutes,

Thus, we get,

⇒θ $=20*\frac{\pi }{30} = \frac{2\pi }{3}$

⇒θ $=\frac{2\pi }{3}$  ______{1}

Next, we are given in the question that the length of the minute hand clock is 2.1 cm which gives us the value of the radius of the clock.

Also, the distance covered by the tip of the minute is given by l .

Thus, we get the formula as θ$=\frac{l}{r}$

Substituting the value of r

in the above formula, we get,

⇒θ $=l*2.1$    ________{2}

 

Now, we will compare equation (1) and (2) to find the value of l .

Thus, we get,

         $\frac{2\pi }{3} = \frac{l}{2.1} \\\\l =\frac{2\pi }{3} * 2.1$

On putting the value of $\pi =\frac{22}{7}$  , we get,

$l=\frac{2}{3} (\frac{22}{7} )*2.1\\\\ =4.4cm$

Thus, we get the value of the tip covered in 20 minutes is 4.4 cm.