Question

The radius of a circle is $3.5$ cm and area of the sector is $3.85$ $c{m}^2$. Find the length of the corresponding arc.

• A. $2.2cm$
• B. $4.2cm$
• C. $5.1cm$
• D. $6.2cm$

Answer 1

The correct option is A $2.2cm$

Let the angle of centre made by the sector be $\theta$
Therefore,
Area of the sector=$\pi r^2\frac{\theta }{360}$
$=>3.85=\frac{\pi (3.5{)}^2\theta }{360}$

$=>\theta =\frac{3.8\times 360\times 7}{(3.5{)}^2\times 22}$
$=35.5$
$=36$
Thus length of the arc =$2\pi r\frac{\theta }{360}$
=$2\times \frac{22}{7}\times 3.5\times \frac{36}{360}$
=$2.2cm$