Calculate the area of the minor segment of a circle of radius 14cm using each of the following angles subtended at this (a)14degree(b)50degree(c)120degree

A≈615.75cm²

I want answer

To calculate the area of the minor segment of a circle, we need to know the radius of the circle and the central angle that subtends the segment.

The formula to calculate the area of a minor segment is given by:

Area = (θ/360) x π x r^2 - (1/2) x r^2 x sin(θ)

Where:
- θ is the central angle in degrees
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the circle

Let's calculate the area for each of the given angles:

(a) For θ = 14 degrees and r = 14 cm:
Area = (14/360) x π x (14)^2 - (1/2) x (14)^2 x sin(14)
= (0.0389) x 3.14159 x (14)^2 - (0.5) x (14)^2 x sin(14)
≈ 10.74 cm^2

(b) For θ = 50 degrees and r = 14 cm:
Area = (50/360) x π x (14)^2 - (1/2) x (14)^2 x sin(50)
= (0.1389) x 3.14159 x (14)^2 - (0.5) x (14)^2 x sin(50)
≈ 37.56 cm^2

(c) For θ = 120 degrees and r = 14 cm:
Area = (120/360) x π x (14)^2 - (1/2) x (14)^2 x sin(120)
= (0.3333) x 3.14159 x (14)^2 - (0.5) x (14)^2 x sin(120)
≈ 96.01 cm^2

Therefore, the area of the minor segment of the circle with a radius of 14 cm is approximately:
(a) 10.74 cm^2
(b) 37.56 cm^2
(c) 96.01 cm^2