A central angle of `40^(@)` in a circle of radius 1 inch intercepts an arc whose length is s. find s.

Options

A. 0.7
B. 1.4
C. 2
D. 3

Explanation

To find the length of the arc \( s \) intercepted by a central angle of \( 40^\circ \) in a circle of radius \( 1 \) inch, we can follow these steps:

### Step 1: Convert the angle from degrees to radians
The formula to convert degrees to radians is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
For our problem, the angle is \( 40^\circ \):
\[ \text{radians} = 40 \times \frac{\pi}{180} \]
Calculating this gives:
\[ \text{radians} = \frac{40\pi}{180} = \frac{2\pi}{9} \]

### Step 2: Use the formula for arc length
The formula for the length of an arc \( s \) is given by:
\[ s = r \times \theta \]
where \( r \) is the radius and \( \theta \) is the angle in radians. Here, the radius \( r = 1 \) inch and \( \theta = \frac{2\pi}{9} \) radians.

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ s = 1 \times \frac{2\pi}{9} \]
This simplifies to:
\[ s = \frac{2\pi}{9} \]

### Step 4: Calculate the numerical value of \( s \)
To find the approximate numerical value, we can use \( \pi \approx 3.14 \):
\[ s \approx \frac{2 \times 3.14}{9} \approx \frac{6.28}{9} \approx 0.6989 \text{ inches} \]

### Final Answer
Thus, the length of the arc \( s \) is approximately \( 0.7 \) inches.

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