Question

What is the area of the Minor segment cut off a circle of radius 10cm by a chord of length 14cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the minor segment cut off a circle of radius 10cm by a chord of length 14cm, we first need to find the central angle corresponding to the chord.

Let the central angle be θ. We can use the formula for the length of a chord in a circle:
chord length = 2r * sin(θ/2)
14 = 2*10*sin(θ/2)
7 = 10*sin(θ/2)
sin(θ/2) = 7/10
θ/2 = sin^(-1)(7/10)
θ ≈ 84.29 degrees

Now we can calculate the area of the segment using the formula:
A = 0.5 * r^2 * (θ - sinθ)
A = 0.5 * 10^2 * (84.29 - sin(84.29))
A = 50 * (84.29 - 0.9989)
A ≈ 418.755 cm^2

Therefore, the area of the minor segment cut off a circle of radius 10cm by a chord of length 14cm is approximately 418.755 cm^2.