A circle has a radius of 8cm. What is the length of an arc with a central angle of 80∘? 80180×𝜋×8cm 802𝜋×8cm 80360×𝜋×8cm
Question
A circle has a radius of 8cm. What is the length of an arc with a central angle of 80∘? 80180×𝜋×8cm 802𝜋×8cm 80360×𝜋×8cm
Solution
The length of an arc (s) in a circle can be calculated using the formula:
s = r * θ
where:
- r is the radius of the circle, and
- θ is the central angle in radians.
However, in this case, the central angle is given in degrees, not radians. To convert from degrees to radians, we can use the conversion factor π radians = 180 degrees. So, the central angle in radians is (80/180) * π = (4/9) * π.
Substituting r = 8 cm and θ = (4/9) * π into the formula gives:
s = 8 * (4/9) * π = (32/9) * π cm
Therefore, the length of the arc with a central angle of 80 degrees in a circle with a radius of 8 cm is (32/9) * π cm.
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