Question : The area of the sector of a circle is 128 cm2. If the length of the arc of that sector is 64 cm, then find the radius of the circle.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 2 cm
Option 4: 16 cm
Correct Answer: 4 cm
Solution : Length of arc = $\frac{ \theta}{360°}\times 2\pi r = 64$ ⇒ $\frac{ \theta}{360°} = \frac{64}{2 \pi r}$ Area of the sector = $\frac{\theta}{360°} \times \pi r^2$ ⇒ $\frac{\theta}{360°} \times \pi r^2 = 128$ ⇒ $\frac{64}{2 \pi r} \times \pi r^2 = 128$ ⇒ $r = \frac{128\times 2}{64}$ ⇒ $r$ = 4 cm Hence, the correct answer is 4 cm.
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