The Arc of a circle of radius 20 cm subtends an angle of 120 degree at the centre. Taking 3.142 for π to calculate the area of the sector correct to the nearest cm square.
π * r^2 * (120º / 360º)
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To calculate the area of the sector, follow these steps:
Step 1: Find the circumference of the circle.
The circumference (C) of a circle is calculated using the formula: C = 2πr, where r is the radius.
Given that the radius (r) is 20 cm and taking π as 3.142, we can calculate the circumference as follows:
C = 2 * 3.142 * 20 cm
C ≈ 125.68 cm (rounded to two decimal places)
Step 2: Calculate the length (L) of the arc.
The length of the arc (L) is calculated using the formula: L = (θ/360) * C, where θ is the angle in degrees and C is the circumference.
Given that the angle (θ) is 120 degrees, we can calculate the length of the arc as follows:
L = (120/360) * 125.68 cm
L ≈ 41.89 cm (rounded to two decimal places)
Step 3: Calculate the area (A) of the sector.
The area of the sector (A) is calculated using the formula: A = (θ/360) * π * r^2, where θ is the angle in degrees, π is the approximate value of pi, and r is the radius.
Given that θ is 120 degrees, π is 3.142, and r is 20 cm, we can calculate the area of the sector as follows:
A = (120/360) * 3.142 * (20 cm)^2
A ≈ 418.68 cm^2 (rounded to two decimal places)
Therefore, the area of the sector, correct to the nearest cm square, is approximately 419 cm^2.
To calculate the area of the sector, we can use the formula:
Area of sector = (θ/360) * π * r²
where θ is the central angle (in degrees), π is approximately 3.142, and r is the radius of the circle.
Let's substitute the given values into the formula:
θ = 120 degrees
π = 3.142
r = 20 cm
Using these values, we can calculate the area of the sector:
Area of sector = (120/360) * 3.142 * (20)^2
= (1/3) * 3.142 * 400
≈ 418.747 cm²
Therefore, the area of the sector is approximately 418.747 cm² when rounded to the nearest square cm.