Question

find the the length of arc subtending an angle of measure 60 at the centre of a circle , whose area is 616cm

Answer 1

Answer: The answer is (A) $\dfrac{44}{3}.$

Step-by-step explanation: As shown in the attached figure, 'C' is a circle with centre 'O' and area 616 cm². AB is an arc on the circle which subtends an angle of 60° at the centre 'O', i.e., ∠AOB=60°.

We are to find the length of arc AB.

Now, total angle subtended at the centre = 360°.

The formula for arc length is given by

$\ell=\dfrac{\textup{angle subtended by the arc}}{\textup{total angle}}\times 2\pi r,$ where $r$ is the radius of the circle.

Also given that

$Area = 616 cm^2\\\\\Rightarrow \pi r^2=616\\\\\Rightarrow r^2=\dfrac{616\times 7}{21}\\\\\Rightarrow r=14~\textup{cm(approx.)}.$

Therefore, length of arc AB is given by

$\ell=\dfrac{60^\circ}{360^\circ}\times 2\pi r=\dfrac{1}{3}\times \dfrac{22}{7}\times 14=\dfrac{44}{3}.$

Thus, the correct option is (A).

Answer 2

Answer is

$\frac{44}{3}$

Hope this helps you