A circle has a radius of
8cm
. Find the length
s
of the arc intercepted by a central angle of
110°
.
you know that the whole circumference is 2πr.
You have only a fraction of that; namely,
110/360 * 2πr
To find the length of the arc intercepted by a central angle, you can use the formula:
s = (θ/360) * 2πr
Where:
- s is the length of the arc
- θ is the measure of the central angle in degrees
- r is the radius of the circle
In this case, the radius (r) of the circle is 8 cm, and the measure of the central angle (θ) is 110°. Plugging these values into the formula, we get:
s = (110/360) * 2π * 8
s = (11/36) * 2π * 8
To solve this expression, we need to calculate the value of π. π (pi) is a mathematical constant and is approximately equal to 3.14159. Let's substitute this value:
s = (11/36) * 2 * 3.14159 * 8
s = (11/36) * 2 * 3.14159 * 8
s = (11/36) * 6.28318 * 8
Finally, we can calculate the value of s:
s ≈ (11 * 6.28318 * 8) / 36
s ≈ (442.11472) / 36
s ≈ 12.28152
Therefore, the length of the arc intercepted by a central angle of 110° is approximately 12.28 cm.