Determine the arc length of a circle with a radius of 8 cm ifa) the central angle is 3.5
Question
Determine the arc length of a circle with a radius of 8 cm if
a) the central angle is 3.5
Solution
The formula to calculate the arc length of a circle is:
Arc length = (central angle/360) * 2πr
where:
- the central angle is in degrees,
- r is the radius of the circle,
- π is a constant approximately equal to 3.14159.
Given:
- central angle = 3.5 degrees,
- r = 8 cm.
Substitute these values into the formula:
Arc length = (3.5/360) * 2 * 3.14159 * 8
Now, calculate the arc length:
Arc length = 0.097222 * 2 * 3.14159 * 8 = 4.88692 cm.
So, the arc length of the circle with a radius of 8 cm and a central angle of 3.5 degrees is approximately 4.89 cm.
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