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Difference between revisions of "2012 AMC 10B Problems/Problem 16"
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To determine the area of the figure, you can connect the centers of the circles to form an equilateral triangle of length 4. Find the area of this triangle to include the figure formed in between the circles. This area is 4sqrt3.
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To determine the area of the figure, you can connect the centers of the circles to form an equilateral triangle of length <math>4</math>. Find the area of this triangle to include the figure formed in between the circles. This area is <math>4\sqrt{3}</math>.
  
  
  
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To find the area of the remaining sectors, notice that the sectors have a central angle of 300 because 60 degrees were "used up" for the triangle. The area of one sector is 2^2 * pi * 5/6 = 10pi/3. Then this area is multiplied by three to find the total area of the sectors (10 pi).
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To find the area of the remaining sectors, notice that the sectors have a central angle of 300 because 60 degrees were "used up" for the triangle. The area of one sector is <math>2^2 \pi * 5/6 = 10\pi/3</math>. Then this area is multiplied by three to find the total area of the sectors (10 pi).
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This result is added to area of the equilateral triangle to get a final answer of 10pi + 4sqrt3.
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This result is added to area of the equilateral triangle to get a final answer of <math>10\pi + 4\sqrt3</math>.
  
 
This means (A) is the right answer.
 
This means (A) is the right answer.

Revision as of 21:15, 16 February 2013

This problem has not been edited in. If you know this problem, please help us out by adding it. Template:Wikify

To determine the area of the figure, you can connect the centers of the circles to form an equilateral triangle of length $4$. Find the area of this triangle to include the figure formed in between the circles. This area is $4\sqrt{3}$.


To find the area of the remaining sectors, notice that the sectors have a central angle of 300 because 60 degrees were "used up" for the triangle. The area of one sector is $2^2 \pi * 5/6 = 10\pi/3$. Then this area is multiplied by three to find the total area of the sectors (10 pi). This result is added to area of the equilateral triangle to get a final answer of $10\pi + 4\sqrt3$.

This means (A) is the right answer.

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