Question

Choose the correct alternative answer for the following question.

If measure of an arc of a circle is 160^° and its length is 44 cm, find the circumference of the circle.

 

Options

• 66 cm

•  44 cm

•  160 cm 

•  99 cm

Answer 1

 The measure of the arc of a circle, θ = 160º 
Let r be the radius of the circle.
Length of the arc = 44 cm

\[\therefore \frac{\theta}{360°} \times 2\pi r = 44\]
\[ \Rightarrow \frac{160° }{360° } \times 2\pi r = 44\]
\[ \Rightarrow 2\pi r = \frac{44 \times 360° }{160° } = 99 cm\]

Thus, the circumference of the circle is 99 cm.