A sector has a central angle of 135° and a radius of 8 cm. Another sector of the same circle has a central angle of \(\dfrac{3\pi}{4}\) radians. What is the ratio of the area of the first sector to the area of the second sector?
1 : 1
Convert the first angle from degrees to radians using \(\theta_{\text{rad}} = \theta_{\text{deg}} \times \dfrac{\pi}{180}\).
\(135^{\circ} = 135 \times \dfrac{\pi}{180} = \dfrac{135\pi}{180} = \dfrac{3\pi}{4} \text{ rad}\)
So both sectors of the same circle have a central angle of \(\tfrac{3\pi}{4}\) radians and the same radius. Therefore their areas are equal.
\(\dfrac{A_{1}}{A_{2}} = 1 : 1\)
Hence the required ratio is 1 : 1.
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