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Question 21

The area of a sector and the length of the arc of the sector are equal in numerical value. Then the radius of the circle is


Correct Answer: 2

Solution

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With angle $$\theta$$ in radians, the sector area is $$\frac{1}{2}r^2\theta$$ and the arc length is $$r\theta$$. Setting these equal and dividing both sides by $$r\theta$$ gives $$\frac{r}{2}=1$$, so $$r=2$$.

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