If the central angle of a circle is 70 degrees and the arc length is 10 cm, what is the length of the radius?
8.18511 cm
To find the length of the radius of a circle when given the central angle and arc length, we can use the formula:
Arc Length = (Central Angle / 360 degrees) × (2π × Radius)
In this case, the central angle is given as 70 degrees and the arc length is 10 cm. We need to find the radius.
Plugging the values into the formula, we can rearrange the equation to solve for the radius:
10 cm = (70 degrees / 360 degrees) × (2π × Radius)
To simplify the equation, first, divide both sides of the equation by (70 degrees / 360 degrees):
10 cm / (70 degrees / 360 degrees) = 2π × Radius
Now, divide both sides of the equation by (2π):
(10 cm / (70 degrees / 360 degrees)) / (2π) = Radius
Simplifying the equation further:
Radius ≈ (10 cm × 360 degrees) / (70 degrees × 2π)
Now, calculate the value of the radius:
Radius ≈ 51.48 cm
Therefore, the length of the radius is approximately 51.48 cm.