Question

Area of sector of a circle with radius 18 cm is 198 cm². The measure of central angle is ______.

Options

• 70°

• 14°

• 140°

• 210°

Answer 1

Area of sector of a circle with radius 18 cm is 198 cm². The measure of central angle is 70°.

Explanation:

Given: r = 18 cm, Area = 198 cm².

Area of sector = `θ/360^circ xx πr^2`

`198 = θ/360^circ xx 22/7 xx 18 xx 18`

`198 = θ/360^circ xx 22/7 xx 324`

`9 = θ/360^circ xx 1/7 xx 324`

`1 = θ /360^circ xx 1/7 xx 36`

`1 = θ xx 1/10 xx 1/7`

`1 = θ/70`

θ = 70°

The measure of the central angle is 70°.