Question

A sector of a circle has a central angle of 120 • and a radius of 7 cm. Another sector of the same circle has a central angle of 2∏/3. What is the ratio of the area of the first sector to the area of the second sector?

• A. 3 : 5
• B. 2 : 3
• C. 1 : 1
• D. 4 : 5

Answer 1

Answer:

C. 1 : 1

Area of a sector is proportional to its central angle (when the radius is the same).

First sector angle:

$120^\circ$

Second sector angle:

$\frac{2\pi}{3} \text{ radians}$

Convert to degrees:

$\frac{2\pi}{3} \times \frac{180^\circ}{\pi}$
$= 120^\circ$

So both sectors have the same central angle and the same radius.

Therefore, their areas are equal.

$\boxed{1:1}$