Question

If the area of a sector of a circle is 577.5 $c{m}^2$ and the length of the corresponding arc is 55 cm, then the radius of the circle is .

• A. 12 cm
• B. 18 cm
• C. 21 cm
• D. 24 cm

Answer 1

The correct option is C 21 cm

We know that,
$\text{Area of a sector}=\frac{\text{Length of the arc}\times \text{Radius}}{2}$
Given, the area of a sector of a circle is 577.5 $c{m}^2$ and the length of the corresponding arc is 55 cm.
$\therefore \text{Radius}=\frac{\text{Area of the sector}\times 2}{\text{Length of the arc}}$
$⟹\text{Radius}=21\text{cm}$