find the length of an arc of a circle whose central angle is 322 degrees and radius is 4km
To find the length of an arc of a circle, we use the formula:
length of arc = (central angle/360) x 2πr
where r is the radius of the circle and π is the mathematical constant pi.
Plugging in the values given in the question, we get:
length of arc = (322/360) x 2π x 4km
Simplifying this expression, we get:
length of arc = (0.8944) x 25.1327 x 4km
length of arc = 8.9292 x 4km
length of arc = 35.7168 km
Therefore, the length of the arc is 35.7168 kilometers.
To find the length of an arc of a circle, you can use the formula:
Arc length = θ/360 * 2πr
where θ is the central angle in degrees, r is the radius, and π is a mathematical constant approximately equal to 3.14159.
Given that the central angle is 322 degrees and the radius is 4 km, let's substitute these values into the formula:
Arc length = (322/360) * 2π(4)
Simplifying further:
Arc length = (0.8944) * 2 * 3.14159 * 4
Arc length = 0.8944 * 6.28318 * 4
Arc length ≈ 22.37 km
Therefore, the length of the arc is approximately 22.37 km.
To find the length of an arc of a circle, you can use the following formula:
Arc length = (angle/360) * 2πr
where:
- angle is the central angle of the arc
- r is the radius of the circle
In this case, the central angle is 322 degrees and the radius is 4 km.
First, convert the angle from degrees to radians by multiplying it by π/180:
322 degrees * (π/180) = 5.63 radians (rounded to two decimal places)
Now, substitute the values into the formula:
Arc length = (5.63/360) * 2π(4 km)
= (0.01564) * 2π(4 km)
≈ 25.13274 km
Therefore, the length of the arc is approximately 25.13 km.