2018 AMC 8 Problems/Problem 15
Problem 15
In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of square unit, then what is the area of the shaded region, in square units?
Solution
Let the radius of the large circle be . Then the radii of the smaller circles are . The areas the circles are directly proportional to the square of the radii, so the ratio of the area of the small circle to the large one is . This means the combined area of the 2 smaller circles is the larger circle, therefore the shaded region is equal to the combined area of the 2 smaller circles, which is
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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