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Bunuel

In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

Attachment:
The attachment 2017-11-17_0946.png is no longer available

Inside square has a an area of 4.
Subtract 2 half pokeballs from 4, so subtract one full pokeball.
Square Area 4 - Pokeball area of 3.1 = .9 shaded or E.
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poke.png
poke.png [ 17.4 KiB | Viewed 5184 times ]

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Bunuel

In the figure above, the circles touch each other and touch the sides of the rectangle at the lettered points shown. The radius of each circle is 1. Of the following, which is the best approximation to the area of the shaded region?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 1

Attachment:
2017-11-17_0946.png

We can see that the area of the shaded region is half the area of the region inside of the rectangle but outside of the two circles. Thus, the area of the shaded region is half the difference between the area of the rectangle and the total area of the two circles.

Area of the rectangle = 2 x 4 = 8

Area of a circle = π x 1^2 = π

Area of shaded region = ½ x (8 - 2π) = 4 - π

Since π is approximately 3.14, the area of the shaded region ≈ 4 - 3.14 = 0.86 ≈ 1.

Answer: E
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Area of rectangle 2x4=8
Are of each circle is π
Area of the segments inside the rectangle that are outside the circles is 8-2π ≈ 2, hence the shaded region has to be less than 2. Only answer E is left.
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