In the figure above, the circles touch each other and touch the sides

Question

https://gmatclub.com/forum/download/file.php?id=38668 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 2017-11-17_0946.png

Luckisnoexcuse · Answer

Length of BC = BF = 2

Area of square BCFE = 4

Area of Circle (unshaded part which overlaps Square) = 2 * 1/2 * pie * r^2 = pie

Shaded region area = 4- pie = ~1

E

generis · Answer

mmmm.png The area of the shaded region equals (Rectangle area) - (circles' area)/2 Rectangle area : L * W The circles' radii completely span the length and width of the rectangle Radius of one circle = 1 LENGTH = 4 radii = 4 WIDTH = 2 radii = 2 Rectangle's area = 4 * 2 = 8 Area of both circles , where r = 1: 2(πr^2) = 2π Area of shaded region The "extra" area between the rectangle's edges and the circles' edges consists of 8 equal regions. See diagram. Four of 8 are shaded = 1/2 of extra is shaded. To get total extra area, subtract circles' area from rectangle's area. To get half the total extra area (shaded region), subtract circles' area from rectangle's area and divide by 2. Half of extra area = area of shaded region : (rectangle area, R ) - (circles' area, C ) divided by 2: \frac{(R - C)}{2} \frac{(8 - 2π)}{2} π\approx{3.14} \frac{(8 - 6.28)}{2}= \frac{1.72}{2} = .86 0.86\approx{1} Answer E

IdiomSavant · Answer

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.

ScottTargetTestPrep · Answer

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

MartinM94 · Answer

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.

bumpbot · Answer

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In the figure above, the circles touch each other and touch the sides

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In the figure above, the circles touch each other and touch the sides

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