Question

In the given figure, O is the centre of circle. XYZ is an arc of the circle subtending an angle of 45° at the centre. If the radius of the circle is 32 cm, then the length of the arc XYZ is:

Options

• 4 π cm

• 8 π cm

• 64 π cm

• 128 π cm

Answer 1

8 π cm

Explanation:

Given: Central angle (θ) = 45°

Radius (r) = 32 cm

Formula: The formula for the length of an arc (L) is:

L = `θ/(360°) xx 2pir`

= `(45°)/(360°) xx 2 xx pi xx 32`

= `1/8 xx 64 pi`

= 8 π cm