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

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.