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A sector has a central angle of 144° and radius 7 cm. Another sector with the same radius has a central angle of \(\frac{4\pi}{5}\) radians. What is the ratio of their areas?

1. 1:1
2. 4:5
3. 5:6
4. 7:8

Correct answer: 1:1

Solution

The area of a sector is proportional to its central angle when the radius is the same. Here, \(144^\circ = \frac{144\pi}{180} = \frac{4\pi}{5}\) radians, so both sectors have equal angles and equal areas. Therefore, the ratio is 1:1.

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