Respuesta :
Question:
A circle has a circumference whose length is 25pi find the length of arc whose central angle 90°
Answer:
The length of arc is 19.625 units
Solution:
Given that,
central angle = 90 degree
Circumference = [tex]25 \pi[/tex]
We know that,
[tex]circumference\ of\ circle = 2 \pi r[/tex]
Therefore,
[tex]25 \pi = 2 \pi r\\\\r = \frac{25}{2} = 12.5[/tex]
The formula for arc length when angle is in degrees is:
[tex]\text{ Arc length } = 2 \pi r \times \frac{\theta}{360}[/tex]
Substituting the given values,
[tex]\text{Arc Length } = 2\times 3.14 \times 12.5 \times \frac{90}{360}\\\\\text{Arc length } = 78.5 \times \frac{1}{4}\\\\\text{Arc Length } = 19.625[/tex]
Thus length of arc is 19.625 units
Answer:
There are 360° in a circle. So, A 90° central angle cuts off an arc which has length 90/360 = 1/4 of the circumference.
Therefore, length of arc = (1/4)(25π) = 25π/4.
Step-by-step explanation:
