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The radius of a circle measures 7 inches. A central angle of the circle measuring 4π/15 radians cuts off a sector. What is the area of the sector? Enter your answer, as a simplified fraction.

 

There's so many formulas I'm so confused lol. Can someone help me get an idea of what formula(s) to use to solve this problem??

 Apr 18, 2020
edited by auxiarc  Apr 18, 2020
 #1
avatar+28021 
+2

Area of WHOLE circle   =  pi r^2  =  49 pi   in2

 

Central angle of  4pi/15   radians is a FRACTION of  the total  of  2 pi radians

      4pi/15  /  2pi     =  2/15   fraction of the TOTAL area

 

2/15  x  49 pi = .........  in2   

 Apr 18, 2020
 #2
avatar+278 
+1

Thank you so much! I wasn't even given that formula.. It's so confusing lol. Thank you again. 

auxiarc  Apr 18, 2020
 #3
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Alright, so I attempted it for myself & I'm still very confused. When I enter what you gave me for the total area, I got 1.315947252 = .133333333.

I'm not sure what I'm doing wrong.. And when I tried to solve for the last part, I got 20.525. But is that the area of the whole circle or the sector? 

auxiarc  Apr 18, 2020
 #4
avatar+28021 
+2

Hmmmm     2/15  * 49 pi = 20.53   in2       via my calculator......

 

Also I used  4pi/15         your question   had   4 pi 15       ....  Which is it supposed to be?

   since it asks for a fraction answer , I'm thinking it might be something different.....

 

    Maybe in terms of pi?

 

  2/15  x 49 pi =   98/15  pi     ( 6  8/15) pi

ElectricPavlov  Apr 18, 2020
edited by ElectricPavlov  Apr 18, 2020
edited by ElectricPavlov  Apr 18, 2020
edited by ElectricPavlov  Apr 18, 2020
 #5
avatar+278 
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Rounded up, right? 

auxiarc  Apr 18, 2020
 #6
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Mine is supposed to be 4π/15. That's my bad, omigosh. I'm sorry, I didn't even realize that until you said something. 

auxiarc  Apr 18, 2020
 #7
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No worries.....   I make a lot of mistakes ! cheeky

ElectricPavlov  Apr 18, 2020
 #8
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Thank you for your time, seriously. With the fraction part, I'm just as confused as you are. It'd just be easier to enter in a decimal in my opinion, but it is what it is lol. I appreciate you helping me :)

 Apr 18, 2020

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