Calculate area and are of the sector which subtend the angle of 120 degrees and radius 7cm use pie as 3.142
a = 1/2 r^2θ = 1/2 * 7^2 * 2π/3 = 51.312 cm^2
Calculate the sector of a circle when substend an angle of 120 at the center of a circle with radius 7cm
To calculate the area of a sector, we can use the formula:
Area of sector = (θ/360) * π * r^2
Where:
θ = central angle in degrees
r = radius of the sector
In this case,
θ = 120 degrees
r = 7 cm
π = 3.142
Let's calculate the area of the sector first:
Area of sector = (120/360) * 3.142 * (7)^2
= (1/3) * 3.142 * 49
= 16.333 cm^2 (rounded to three decimal places)
Now, let's calculate the area of the corresponding circle:
Area of circle = π * r^2
= 3.142 * (7)^2
= 153.958 cm^2 (rounded to three decimal places)
Therefore, the area of the sector is approximately 16.333 cm^2 and the area of the corresponding circle is approximately 153.958 cm^2.
To calculate the area and arc length of a sector, you will need to use the given angle and radius. Let's break it down step by step.
1. Given information:
- Angle of the sector = 120 degrees
- Radius of the sector = 7 cm
- Value of π (pi) = 3.142
2. Calculating the area of the sector:
The formula to calculate the area of a sector is given as:
Area = (θ/360) x π x r²
Substitute the values into the formula:
Area = (120/360) x 3.142 x (7)^2
Area = (1/3) x 3.142 x 49
Area = 51.127 cm² (rounded to three decimal places)
Therefore, the area of the sector is approximately 51.127 cm².
3. Calculating the arc length of the sector:
The formula to calculate the arc length of a sector is given as:
Arc Length = (θ/360) x 2π x r
Substitute the values into the formula:
Arc Length = (120/360) x 2 x 3.142 x 7
Arc Length = (1/3) x 6.284 x 7
Arc Length = 14.768 cm (rounded to three decimal places)
Therefore, the arc length of the sector is approximately 14.768 cm.
In summary:
- The area of the sector is approximately 51.127 cm².
- The arc length of the sector is approximately 14.768 cm.