anonymous
  • anonymous
Find the area of the sector of a circle with a central angle of 5 radians and a radius of 5 feet. please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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DebbieG
  • DebbieG
Do you know the sector area formula? \[\Large A=\frac{ \alpha }{ 2 }\cdot r^2\]
anonymous
  • anonymous
so the answer is 62.5?
DebbieG
  • DebbieG
That's what I get. :) do you want an easy way to remember the formula?

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anonymous
  • anonymous
yay! and sure!
DebbieG
  • DebbieG
Think of it as: \(\Large A=\dfrac{ \alpha }{ 2\pi }\cdot \pi r^2\) Because really, all you're doing is taking a PROPORTION of the TOTAL AREA of the circle,right? So look at my "version" of the formula: \(\Large \dfrac{ \alpha }{ 2\pi }\) this is the PROPORTION that the angle \(\alpha\) "cuts out" from the WHOLE circle (since the "angle" of the whole circle is \(2\pi\)). \(\Large \pi r^2\) is the total area of the circle (plain ol' area of a circle formula) so you get proportion x whole: \(\Large A=\dfrac{ \alpha }{ 2\pi }\cdot \pi r^2=\dfrac{ \alpha }{ 2 }\cdot r^2\) because the pi's cancel... but it's an easy way to remember it (and to have an intuitive grasp of the formula). :)
DebbieG
  • DebbieG
And if you are also doing arc length, that's just a PROPORTION of the TOTAL CIRCUMFERENCE so you can use the same idea: \(\Large s=\dfrac{ \alpha }{ 2\pi }\cdot 2\pi r=\alpha r\) The \(2\pi 's\) cancel, but it is intuitively the same thing (portion of circumference).
anonymous
  • anonymous
thank you!!! but what if it asks a question like..what is the exact radian measure of the acute angle formed by the hands of a clock at 7:00? which formula do you use
DebbieG
  • DebbieG
Are you sure it says "ACUTE" angle?? You just need to think about what the face of a clock looks like at 7:00..... |dw:1378667082102:dw| The angle is 7/12 of the whole circle, so what is that in radians? (that's a proportion of 2pi) But it isn't acute!
anonymous
  • anonymous
it says acute, haha that's why it confused me
DebbieG
  • DebbieG
OOPS, it's isn't 7/12 of the circle, it is 5/12 of the circle - that's what I meant to say. That's stil not an acute angle... but I think it is trying to say, the angle that is rotated in the "shortest" direction... e.g.: |dw:1378667322239:dw|
anonymous
  • anonymous
so do you put 5/12 in radians?
DebbieG
  • DebbieG
Well, kind of... it's 5/12 of the WHOLE circle. the WHOLE circle is 2pi radians. So you want 5/12 of 2pi. :)
anonymous
  • anonymous
thank you :) but how do you find that?
DebbieG
  • DebbieG
\[\Large \dfrac{ 5 }{12 }\cdot 2\pi\]
DebbieG
  • DebbieG
"a proportion of the whole" means to multiply the proportion x the whole
anonymous
  • anonymous
is it 2.61?
DebbieG
  • DebbieG
You are using a calculator, which is not an "exact" radian measure... :) Just simplify that product, your answer will be a fraction and will include pi.
anonymous
  • anonymous
10pi/12? sorry, im not the best at math

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