A sector of a circle has a radius of 21cm and an area of 280cm^2 calculate correct to one decimal place the perimeter of the sector
To find the perimeter of the sector, we need to find the arc length of the sector and add it to the sum of the radii.
First, let's find the angle of the sector using the formula for the area of a sector:
Area of sector = (θ/360) * π * r^2
280 = (θ/360) * π * 21^2
280 = (θ/360) * 441π
θ/360 = 280 / (441π)
θ/360 ≈ 0.22459
θ ≈ 0.22459 * 360
θ ≈ 80.8 degrees
Now, let's find the arc length of the sector:
Arc length = (θ/360) * 2 * π * r
Arc length = (80.8/360) * 2 * π * 21
Arc length = 0.22444 * 2 * π * 21
Arc length ≈ 29.8 cm
Finally, let's find the perimeter of the sector by adding the arc length to the sum of the radii:
Perimeter = 29.8 + 21 + 21
Perimeter = 71.8 cm
Therefore, the perimeter of the sector is approximately 71.8 cm.