Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. [...

Answer Details

The formula for the length of an arc of a circle is given by:

L = (θ/360) x 2πr

where θ is the angle subtended at the centre of the circle in degrees, r is the radius of the circle, and π is pi.

Using the given values, we have:

θ = 75°
r = 3.5cm
π = 22/7

Substituting these values into the formula, we get:

L = (75/360) x (2 x 22/7 x 3.5)
L = (5/24) x (44/7)
L = 110/24
L ≈ 4.58cm (correct to 2 significant figures)

Therefore, the length of the arc of the circle is approximately 4.58cm. The correct option is (b) 4.6cm.