The arc of a circle of radius 20cm subtends an angle of 120° at the centre.use the value π to calculate the area of the sector correct to the nearest cm square
The angle of the sector is 120° out of 360°, so the fraction of the circle's area in the sector is:
120°/360° = 1/3
The area of the full circle is:
πr^2 = π(20cm)^2 = 400π cm^2
So the area of the sector is:
(1/3) x 400π cm^2 = 133.33π cm^2
To find this value to the nearest cm^2, we need to round it.π is approximately 3.14, so:
133.33π cm^2 ≈ 133.33 x 3.14 cm^2 ≈ 419.6262 cm^2
Rounding to the nearest cm^2 gives:
419 cm^2.
Therefore, the area of the sector, correct to the nearest cm square, is 419 cm^2.