Question

What is the area of minor segment cut off a circle of radius 10 cm by a cord of 14 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the minor segment cut off by a circle of radius 10 cm and a cord of 14 cm, we first need to find the angle at the center of the circle that the cord subtends.

Using the formula for the angle at the center of a circle subtended by a cord:

angle = 2 * arcsin(cord / (2 * radius))
angle = 2 * arcsin(14 / (2 * 10))
angle = 2 * arcsin(0.7)
angle = 2 * 44.43 degrees
angle = 88.87 degrees

Now, we can calculate the area of the minor segment using the formula:

Area = (r^2 / 2) * (θ - sin(θ))
Area = (10^2 / 2) * (88.87 - sin(88.87))
Area = (100 / 2) * (88.87 - 0.777)
Area = 50 * 88.09
Area = 4404.5 cm^2

Therefore, the area of the minor segment cut off by a circle of radius 10 cm and a cord of 14 cm is 4404.5 cm^2.