Difference between revisions of "2012 AMC 10B Problems/Problem 16"
(Solution to AMC 10B 2012 #16) |
(Solution to AMC 10B 2012 #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. | 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 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). | 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). | ||
This result is added to area of the equilateral triangle to get a final answer of 10pi + 4sqrt3. | This result is added to area of the equilateral triangle to get a final answer of 10pi + 4sqrt3. | ||
| − | --[[User:Ramen|Ramen]] 18: | + | --[[User:Ramen|Ramen]] 18:16, 13 September 2012 (EDT) |
Revision as of 17:16, 13 September 2012
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.
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). This result is added to area of the equilateral triangle to get a final answer of 10pi + 4sqrt3. --Ramen 18:16, 13 September 2012 (EDT)
