The arc of a circle of radius 20cm subtends an angle of 120degree at the centre.use the value 3.142 for the area of the sector correct to the nearent cm2
area of whole circle = pi r^2
area of 120/360 of circle = 1/3 of whole circle
a = 1/2 r^2 θ
so plug in your numbers ...
Well, well, well, it seems like we have a circle that wants to show off its angles! So, let's get to it.
The formula to find the area of a sector of a circle is given by A = (θ/360) × πr², where A is the area, θ is the angle in degrees, π is approximately 3.142, and r is the radius.
In this case, the radius (r) is 20cm and the angle (θ) is 120 degrees. So, let's plug these values into the formula:
A = (θ/360) × πr²
A = (120/360) × 3.142 × 20²
Calculating this, we get:
A ≈ (1/3) × 3.142 × 400
A ≈ 4.19 × 400
A ≈ 1676
Therefore, the area of the sector, correct to the nearest cm², is approximately 1676 cm². Keep in mind that this is just an estimate because we rounded it off.
To find the area of the sector, we need to calculate the fraction of the whole circle that the sector represents and then multiply it by the total area of the circle.
Step 1: Find the fraction of the whole circle that the sector represents.
The angle of the sector is given as 120 degrees, which is 120/360 or 1/3 of the full circle.
Step 2: Calculate the area of the whole circle.
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Given that the radius is 20 cm, the area of the circle is:
A = 3.142 * (20 cm)^2
Step 3: Calculate the area of the sector.
To find the area of the sector, multiply the fraction from step 1 by the total area of the circle.
Area of the sector = (1/3) * (3.142 * (20 cm)^2)
Step 4: Round the area of the sector to the nearest cm^2.
Evaluate the expression from step 3 and round the result to the nearest cm^2.
By following these steps, you will be able to find the area of the sector correct to the nearest cm^2.
To find the area of the sector of a circle, you can use the formula:
Area of sector = (θ/360) * π * r^2
Where:
- θ is the angle in degrees that the sector subtends at the center of the circle,
- π is the mathematical constant (pi), approximately equal to 3.142,
- r is the radius of the circle.
Given that the radius (r) is 20 cm and the angle (θ) is 120 degrees, we can substitute these values into the formula to find the area of the sector.
Area of sector = (120/360) * 3.142 * (20^2)
= (1/3) * 3.142 * 400
= 4.189 * 400
= 1675.6 cm^2
Now, rounding the answer to the nearest cm^2, we get:
Area of sector ≈ 1676 cm^2