Calculate the area of a sector of a circle which subtends an angle of 45 degree at the center of the circle, radius 14cm.
Explain how to get the radius
To calculate the area of the sector, use the formula:
Area of sector = (angle/360) x πr²
where angle is the measure of the angle subtended by the sector, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
Plugging in the given values, we get:
Area of sector = (45/360) x π(14)²
Area of sector = (1/8) x 196π
Area of sector = 24.5π square cm, or approximately 76.93 square cm (rounded to two decimal places)
To get the radius of the circle, it may have been given in the problem statement. If not, it can be measured using a ruler or other measuring device. Alternatively, if the circumference of the circle is known, the radius can be calculated using the formula:
Circumference = 2πr
r = Circumference/(2π)
where Circumference is the distance around the circle.
To calculate the area of a sector, you need to know the radius of the circle and the central angle subtended by the sector.
Given that the radius of the circle is 14 cm and the central angle is 45 degrees, you can follow these steps to calculate the area of the sector:
1. Convert the central angle from degrees to radians. Since the formula for calculating the area of a sector requires the angle to be in radians, divide the angle by 180 and multiply by π (pi). In this case, the angle is 45 degrees, so the conversion to radians is (45/180) * π = 0.25π radians.
2. Use the formula for the area of a sector: Area = (angle/360) * π * r^2. Substituting the values, the formula becomes (0.25π/360) * π * (14^2).
3. Simplify the expression: (0.25/360) * π^2 * 196.
4. Calculate the value: (0.25/360) * 3.1416^2 * 196 ≈ 3.14 * 196 ≈ 615.44 cm^2.
Therefore, the area of the sector is approximately 615.44 cm^2.
To find the radius of a circle, you need to measure the distance from the center of the circle to any point on its circumference. In this case, the radius is given as 14 cm.