Question

The measure of an arc of a circle is $ {60^0} $ and its radius is $ 15cm $ . Find the length of the arc. $ (\pi = 3.14) $

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since we need to find the length of the arc, $ \theta $ is the angle that in n degree subtended by the angle of the arc which makes a center of the circle.
And three-sixty degrees is a complete angle of the circle starting from zero degrees.
Also, in circle rotation zero degrees and three-sixty degrees are the same; because they will be the starting and ending points of the circle.
Formula used: The length of the arc is $ 2\pi r\dfrac{\theta }{{360}} $

Complete step by step answer:
From the given question the $ \theta $ is given as sixty degrees, and the radius is fifteen centimeters.
Radius is the half of the diameter which is represented as $ r = \dfrac{d}{2} $ .
Also, the pie can be written as the value of $ (\pi = 3.14) $ .
Thus, we have the radius of the arc, the degree that is required, and pie values.
Hence substitute every known value into the formula of the length of the arc, which is $ 2\pi r\dfrac{\theta }{{360}} $ .
Therefore, $ 2\pi r\dfrac{\theta }{{360}} = 2(3.14)(15)\dfrac{{60}}{{360}} $ first canceling the degrees we get $ \dfrac{{60}}{{360}} = 0.166.. $ the degree.
Now apply the degree we found into the simplification we get $ 2\pi r\dfrac{\theta }{{360}} = 2(3.14)(15)(0.1666) $ .
Thus, by the use of multiplication, we simplify the equation $ 2\pi r\dfrac{\theta }{{360}} \Rightarrow 6.26 \times 2.499 $ (first two and last two terms multiplied).
Hence, we get $ 2\pi r\dfrac{\theta }{{360}} = 95.246cm $ .
Hence the length of the arc is $ 95.246cm $.

Note: Since pie $ (\pi = 3.14) $ is an irrational number; because pie is not in the form of $ \dfrac{p}{q},q \ne 0 $ and it is consisting of the fraction’s terms.
Also, the length of the arc is the required answer in this problem; but we are also able to find the radius or degrees using the same formula and methods if the given is the length of the arc.