the circumference of a circle is 60 cm. what is the length of an arc of 140?
if you mean 140° then it would be
60 cm * 140/360 = 23.333 cm
To find the length of an arc on a circle, you need to know the measure of the arc in degrees and the circumference of the circle. In this case, you are given the circumference of the circle as 60 cm.
To find the length of the arc, you can use the formula:
Arc Length = (Arc Measure / 360) * Circumference
In this case, the arc measure is given as 140 degrees.
Plugging in the values, the formula becomes:
Arc Length = (140 / 360) * 60
To simplify further:
Arc Length = (7/18) * 60
Arc Length = 7 * 10/3
Arc Length = 70/3
So, the length of the arc is approximately 23.33 cm.
To find the length of an arc, you need to know two things: the angle subtended by the arc at the center of the circle, and the radius or circumference of the circle.
In this case, we are given the circumference of the circle, which is 60 cm. The formula for finding the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Since we are given the circumference, we can find the radius using the formula r = C/(2π). Substituting the given circumference of 60 cm into the formula, we have r = 60/(2π).
Next, we need to find the length of the arc. The formula for finding the length of an arc is L = (θ/360) x 2πr, where L is the length of the arc, θ is the angle subtended by the arc at the center of the circle (in degrees), and r is the radius.
In this case, we are given the angle θ as 140 degrees. Substituting the values into the formula, we have L = (140/360) x 2πr.
Now, let's calculate the length of the arc using the given information.
1. Find the radius:
r = 60/(2π) ≈ 9.55 cm
2. Calculate the length of the arc:
L = (140/360) x 2π x 9.55 ≈ 21.17 cm
Therefore, the length of the arc with an angle of 140 degrees in a circle with a circumference of 60 cm is approximately 21.17 cm.