Question

A sector of a circle has an area of 32πcm^2 and contains a central angle of 210 degrees.calculate the length of the cord that subtends the angle given above

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the chord, we first need to find the radius of the circle.

The formula for the area of a sector of a circle is given by:

Area = (θ/360)πr^2

Where θ is the central angle in degrees, r is the radius of the circle.

Given that the area of the sector is 32π cm^2 and the central angle is 210 degrees, we have:

32π = (210/360)πr^2

Solving for r, we get:

r^2 = (32*360)/(210)

r^2 = 55.4286

r ≈ √55.4286
r ≈ 7.451

Now, we can find the length of the chord using the formula:

Chord length = 2r sin(θ/2)

Chord length = 2*7.451 * sin(210/2)
Chord length ≈ 2*7.451 * sin(105)
Chord length ≈ 2*7.451 * 0.9659
Chord length ≈ 14.902 * 0.9659
Chord length ≈ 14.398 cm

Therefore, the length of the chord that subtends the angle of 210 degrees is approximately 14.398 cm.