Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answers
Given:
enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi
To find:
Find the arc length of the semicircle.
Solution:
The interior angle of a circle equals 360°
Therefore, the central angle of a semicircle equals 360°/2 = 180°
The proportion of the length of the arc, x, to the circumference of the circle is equal to the proportion of the central angle to 360 degrees.
x / 2πr = 180° / 360°
x = 180° / 360° × 2πr
x = 1/2 × 2 × π × r
x = πr
Since radius value isn't given, taken "r"
Answer:
The arc length of the semicircle is 5π units.
(Note that we could also multiply 5 by 3.14 to get 15.7 units.)
Step-by-step explanation:
We want to find the arc length of 1/2
Let's start by finding the circumference of the circle.
Circumference of the circle =2πr
=2πr
=2π⋅5
=5⋅2π
=10π
The arc length is 1/2 of the circumference of the circle.= 1/2⋅10π
= 10/2π
= 5π