Question

The length of the arc subtending an angle of 210° at the centre of the circle is `44/3` cm. The radius of the circle is ______.

Options

• `2sqrt(2)` cm

• 4 cm

• 8 cm

• `1/4` cm

Answer 1

The length of the arc subtending an angle of 210° at the centre of the circle is `44/3` cm. The radius of the circle is 4 cm.

Explanation:

The length of the arc = `44/3` cm

The angle subtended by the arc = 210°

We know that the length of arc is

`l = θ/360 xx 2πr`

⇒ `44/3 = 210/360 xx 2 xx 22/7 xx r`

⇒ `44/3 = 21/18 xx 2 xx 11/7 xx r`

⇒ `44/3 = 1/3 xx 11 xx r`

⇒ `44/3 xx 3/1 = 11 xx r`

⇒ 44 = 11 × r

⇒ `44/11` = r

⇒ r = 4 cm