# Choose the Correct Alternative Answer for the Following Question. the Ratio of Circumference and Area of a Circle is 2:7. Find Its Circumference. - Geometry

#### Question

Choose the correct alternative answer for the following question.
The ratio of circumference and area of a circle is 2:7. Find its circumference.
##### Options
• $14\pi$

•   $\frac{7}{\pi}$

• 7$\pi$

• $\frac{14}{\pi}$

#### Solution

Let r be the radius of the circle.
Circumference of the circle : Area of the circle = 2 : 7

$\Rightarrow \frac{2\pi r}{\pi r^2} = \frac{2}{7}$
$\Rightarrow \frac{1}{r} = \frac{1}{7}$
$\Rightarrow r = 7$

∴ Circumference of the circle =  $2\pi r = 2\pi \times 7 = 14\pi$

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