May 18th, 2017, 03:57 PM  #1 
Member Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2  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? 
May 18th, 2017, 04:21 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,249 Thanks: 292  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. 
May 18th, 2017, 04:22 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,473 Thanks: 884 Math Focus: Elementary mathematics and beyond 
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. 
May 18th, 2017, 06:53 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,035 Thanks: 620  

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