A sector of a circle of radius 7cm,substend angle 270°at the center . Calculate the length of the arc
To calculate the length of the arc of a sector, you need to use the formula:
Length of arc = (angle/360) * 2πr
where angle is the measure of the angle subtended by the sector at the center of the circle, and r is the radius of the circle.
In this case, the angle is given as 270°, so we can substitute the values into the formula:
Length of arc = (270/360) * 2π * 7
Simplifying this equation:
Length of arc = (3/4) * 2π * 7
Now, let's calculate the length of the arc:
Length of arc = (3/4) * 2 * 22/7 * 7
= (3/4) * 2 * 22
= (3/4) * 44
= 33 cm
Therefore, the length of the arc is 33 cm.