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May 18th, 2017, 03:57 PM   #1
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Area of segment

In a circle, a sector subtends at an angle of 1 radian at the centre, If the are if the segment is 8cm^2 find its perimeter.

I understand that 1 radian = 57 degrees

But where do I go next?
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May 18th, 2017, 04:21 PM   #2
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Originally Posted by Posher View Post

I understand that 1 radian = 57 degrees
In math we never write an equal sign unless two things are equal. This will keep you from many mistakes

$2 \pi$ radians = $360$ degrees, therefore $1$ radian = $\frac{360}{2\pi} = \frac{180}{\pi} \approx 57.2957795130823$ degrees.

If you are doing a practical calculation, your estimate is handy to know. But they're not equal.

Last edited by Maschke; May 18th, 2017 at 04:23 PM.
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May 18th, 2017, 04:22 PM   #3
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We have a sector of area $8\,\text{cm}^2$ and a section of arc subtended by 1 radian. The ratio of the sector to the area of the circle is equal to the ratio of the subtended arc to the measure of the circumference of the circle.

$$\frac{8}{\pi r^2}=\frac{1}{2\pi}\implies r=4$$

As the length of arc subtended by 1 radian is equivalent to the radius of the circle and $3r=12$, the perimeter of the sector is $12\text{ cm}$.

Last edited by greg1313; May 21st, 2017 at 09:49 AM.
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May 18th, 2017, 06:53 PM   #4
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