Choose the Correct Alternative Answer for Each of the Following Questions. (2) If Measure of an Arc of a Circle is 160° and Its Length is 44 Cm, Find the Circumference of the Circle. - Geometry

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.

• 66 cm

•  44 cm

•  160 cm

•  99 cm

Solution

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.

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