An arc of a circle subtends an angle of 30o
on the
circumference of a circle of radius 21cm. Find the
length of the arc.
A. 11cm
B. 22cm
C. 44cm
D. 66cm
To find the length of the arc, we need to use the formula for the arc length:
arc length = (angle/360) * 2 * π * radius
Given that the angle is 30° and the radius is 21 cm, we can plug these values into the formula:
arc length = (30°/360) * 2 * π * 21 cm
Simplifying the fraction:
arc length = (1/12) * 2 * π * 21 cm
Multiplying:
arc length = (1/6) * π * 21 cm
Now, we can calculate the approximate value of π using 3.14:
arc length ≈ (1/6) * 3.14 * 21 cm
arc length ≈ 3.49 cm
Therefore, the length of the arc is approximately 3.49 cm.
None of the answer choices A, B, C, D match this value, so it seems there might be an error in the question or the answer choices.
To find the length of the arc, we use the formula:
Length of arc = (angle/360) * 2 * π * radius
Given that the angle of the arc is 30 degrees and the radius of the circle is 21 cm, we can substitute these values into the formula:
Length of arc = (30/360) * 2 * π * 21
Simplifying this expression:
Length of arc = (1/12) * 2 * 3.1416 * 21
Length of arc = 6.2832 * (1/12) * 21
Length of arc = 3.1416 * 21/2
Length of arc = 66.1386 cm
Therefore, the length of the arc is approximately 66 cm, which is option D.