Area of major segment of a circle having centre o n radius 7 is 115.5 find length of corresponding arc

To find the length of the corresponding arc, we first need to calculate the measure of the central angle that corresponds to the major segment.

Step 1: Calculate the area of the entire circle.
The formula to calculate the area of a circle is A = πr², where A represents the area and r represents the radius.

Given that the radius is 7, we can calculate the area of the entire circle using the formula:
A = π * (7)² = 49π

Step 2: Determine the central angle.
The central angle can be found by dividing the area of the major segment by the area of the entire circle and then multiplying by 360°.

Given that the area of the major segment is 115.5 and the area of the entire circle is 49π, we can calculate the central angle as follows:
Central angle = (115.5 / (49π)) * 360°

Step 3: Calculate the length of the corresponding arc.
The formula to calculate the length of an arc is L = (Θ/360°) * 2πr, where L represents the length of the arc, Θ represents the central angle, and r represents the radius.

Using the previously calculated central angle (Θ) and the given radius (r = 7), we can calculate the length of the corresponding arc:
Length of arc = (Central angle / 360°) * 2πr

Substituting the values, we get:
Length of arc = ((Central angle / 360°) * 2π) * 7

By evaluating the expression, you can find the length of the corresponding arc.