The arc of a circle of radius 20cm subtends an angle of 120degree at the center.use the value 3.142 for pie to calculate the area of the sector correct to the nearest cmsquared
area of whole circle = Pi(20)^2
= 400Pi
Using a simple ratio:
A/400Pi = 120/360
A = 400Pi/3 cm^2
= ....
😴😴😴😴😴😡
418.9 centimetres squared
Head boy
To find the sectoral angle, we can use the formula:
Area of sector = (sectoral angle / 360) x pi x radius^2
Substituting the given values, we get:
396 = (sectoral angle / 360) x 3.142 x 20^2
Simplifying and solving for the sectoral angle:
sectoral angle = (396 x 360) / (3.142 x 20^2)
sectoral angle = 214.45 degrees
Therefore, the sectoral angle is 214.5 degrees (correct to 1 decimal place).
To calculate the area of a sector, you can follow these steps:
1. First, find the circumference of the circle. The formula for the circumference is C = 2Ï€r, where "C" denotes the circumference, "Ï€" represents the value of pi (approximately 3.142), and "r" represents the radius of the circle. In this case, the radius is given as 20 cm, so the circumference is C = 2 * 3.142 * 20 = 125.68 cm (rounded to two decimal places).
2. Next, calculate the fraction of the circle's circumference that is subtended by the given angle of 120 degrees. The fraction is found by dividing the angle (in degrees) by the total angle in a circle (360 degrees). In this case, the angle is 120 degrees, so the fraction is 120/360 = 1/3.
3. To find the length of the arc of the sector, multiply the fraction obtained in step 2 by the circumference of the circle calculated in step 1. The length of the arc is (1/3) * 125.68 = 41.89 cm (rounded to two decimal places).
4. Finally, calculate the area of the sector using the formula A = (θ/360) * π * r^2, where "A" denotes the area, "θ" represents the angle (in degrees), "π" represents the value of pi (approximately 3.142), and "r" represents the radius of the circle. In this case, the angle is 120 degrees, so the area of the sector A = (120/360) * 3.142 * 20^2 = 209.73 cm^2 (rounded to two decimal places).
Therefore, the area of the sector is approximately 209.73 cm^2 when rounded to the nearest cm^2.