Question

The length of minor arc $AB$ of circle with area $81\pi$ square units and $\angle ACB=$${120}^{\circ }$ is

• A. $6\pi$
• B. $9\pi$
• C. $18\pi$
• D. $27\pi$

Answer 1

The correct option is A $6\pi$

Area of circle $AB=$ $81\pi$
$\Rightarrow 81\pi =\pi r^2$
$\Rightarrow r^2=9$
$\Rightarrow r=9$
Length of the arc $=$ $2\pi r\frac{\angle ACB}{360}$
$=$ $2\pi \times 9\times \frac{120}{360}$
Length of the arc $=$ $6\pi$