Question 1186235: beginning at the origin a spiral is constructed from three semmi-circles with centres at (1,0), (0,0) and (2,0) the are of the shaded region in u^2 is?
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Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to find the area of the shaded region:
**1. Visualize the shape:**
Imagine the three semicircles. The first has a center at (1,0) and extends from x=0 to x=2. The second has a center at (0,0) and extends from x=0 to x=1. The third has a center at (2,0) and extends from x=1 to x=2. The shaded area is the combination of all three.
**2. Recognize the components:**
Notice that the three semicircles together form a full circle with radius 1.
**3. Calculate the area:**
The area of a circle is given by the formula A = πr², where r is the radius. In this case, r = 1.
Area = π * 1² = π
Therefore, the area of the shaded region is **π** square units, which is approximately **3.1416** square units.
Answer by ikleyn(52866)  (Show Source):
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