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

Answer 1

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.