Final answer:
To calculate the area of a segment of a circle with radius 14 cm and subtends an angle of 180°, we find half of the area of the full circle by using the formula A = πr², resulting in 308 cm² correct to one decimal place.
Step-by-step explanation:
To calculate the area of a segment of a circle whose radius is 14cm and subtends an angle of 180° at the centre, we'll use the formula for the area of a circle: A = πr². Since the angle of the segment is 180°, which is half of a full circle (360°), the area of the segment is half the area of the circle.
Given:
- Radius (r) = 14 cm
- Angle (θ) = 180°
First, we calculate the area of the full circle:
A full circle = π × r² = π × (14 cm)²
Then, since the angle is 180° which is half of 360°, we take half of the full circle's area:
Area of a segment = ½ × A full circle = ½ × π × 196 cm²
Area of a segment = 0.5 × π × 196 cm²
Area of a segment = 98π cm²
Using π ≈ 3.14159, we get:
Area of a segment ≈ 98 × 3.14159 cm² ≈ 307.88 cm²
To follow significant figures rules, since the radius is given to two significant figures, the area should also be represented with two significant figures, which rounds the area to 308 cm² when given to one decimal place.