An object moved in a circular path of radius 21m such that it made an angle of 30°. What is the distance (in meter) covered by the object?
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Correct Answer: Option A
Explanation:
To find the distance covered by an object moving in a circular path, you need to calculate the arc length. The formula for the arc length \( s \) of a circle is:
\[ s = r \theta \]
where:
- \( r \) is the radius of the circle
- \( \theta \) is the angle in radians
First, convert the angle from degrees to radians:
\[ \theta = \frac{30^\circ \times \pi}{180^\circ} = \frac{\pi}{6} \]
Now, use the formula to find the arc length:
\[ s = r \times \theta \]
\[ s = 21 \times \frac{\pi}{6} \]
\[ s = 21 \times \frac{3.14}{6} \]
\[ s \approx 21 \times 0.523 \]
\[ s \approx 10.98 \]
Rounded to the nearest meter, the distance covered is approximately 11 meters.
So, the correct answer is:
A. 11m
To find the distance covered by an object moving in a circular path, you need to calculate the arc length. The formula for the arc length \( s \) of a circle is:
\[ s = r \theta \]
where:
- \( r \) is the radius of the circle
- \( \theta \) is the angle in radians
First, convert the angle from degrees to radians:
\[ \theta = \frac{30^\circ \times \pi}{180^\circ} = \frac{\pi}{6} \]
Now, use the formula to find the arc length:
\[ s = r \times \theta \]
\[ s = 21 \times \frac{\pi}{6} \]
\[ s = 21 \times \frac{3.14}{6} \]
\[ s \approx 21 \times 0.523 \]
\[ s \approx 10.98 \]
Rounded to the nearest meter, the distance covered is approximately 11 meters.
So, the correct answer is:
A. 11m