Question

What is the exact area of the major segment of a circle of diameter 14 cm in which the Minor segment subtends an angle of 5π÷6 radians

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the major segment of a circle, we first need to calculate the area of the sector formed by the minor segment subtending an angle of 5π/6 radians.

The area of a sector of a circle with radius r and central angle θ is given by:

Area = (θ/2π) * πr^2
= θr^2/2

In this case, the radius of the circle is 14/2 = 7 cm, and the central angle is 5π/6 radians. So, the area of the sector formed by the minor segment is:

Area_minor = (5π/6) * 7^2 / 2
= (35π / 6) * 7 / 2
= 122.5 cm^2

Now, the area of the major segment of the circle is the difference between the area of the circle and the area of the segment formed by the minor segment. The area of the circle is given by:

Area_circle = πr^2
= π * 7^2
= 49π cm^2

Therefore, the area of the major segment is:

Area_major = Area_circle - Area_minor
= 49π - 122.5
≈ 41.5 cm^2

So, the exact area of the major segment is approximately 41.5 cm^2.

Answer 2

"exact area of the major segment is approximately" makes no sense.

In fact, the exact area is
49π - (5π/6) * 7^2 / 2 = 343/12 π

Answer 3

[AI-generated answer — Bot GPT 3.5]

You are correct.

The exact area of the major segment of a circle with a diameter of 14 cm in which the minor segment subtends an angle of 5π/6 radians is indeed 343/12 π square cm.