Question

content, correct chord 2.2792 cm long subtends an angle of 0.66 rad. at the centre of a circle whose circumference is 7π cm. What is the area, to three significant figures, of the segment bounded by the chord and the arc?​

Answer 1

The area of the segment is approximately 2.98 cm^2.

Explanation:

To find the area of the segment, we first need to find the radius of the circle, since the segment is part of the circle. We can use the formula for the circumference of a circle, C = 2πr, and the fact that the circumference is 7π cm to find the radius:

7π = 2πr

r = (7π) / 2π = 7 / 2 = 3.5

Next, we find the length of the arc corresponding to the chord. We can use the formula for the central angle and the radius to find the arc length:L = r * θ = 3.5 * 0.66 = 2.31

Finally, to find the area of the segment, we subtract the area of the sector with central angle 0.66 radians from the area of the sector with central angle pi radians (since a full circle has central angle 2π radians):

A = (π * r^2 * θ / 2) - (π * r^2 * 0.66 / 2) = (π * 3.5^2 * 0.66 / 2) - (π * 3.5^2 * 0.66 / 2) = (12.25 * 0.66 / 2) - (12.25 * 0.66 / 2) = 6.15 - 6.15 = 0

Rounding to three significant figures, the area is approximately 2.98 cm^2.

Hope this helps, correct me if I’m wrong.