If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€
Answer: D
Difficulty level: 700+
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If each of the 4 circles above has radius 1, what
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If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€
Answer: D
Difficulty level: 700+
Source: www.gmatprepnow.com
Brent Hanneson - Creator of GMATPrepNow.com
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GMATGuruNY
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Brent@GMATPrepNow wrote:
If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€
Area of the blue square above = s² = 2² = 4.
Area of each circle = πr² = π(1²) = π.
Each unshaded portion in the blue square constitutes 1/4 of a circle.
Thus, the 4 unshaded portions combined constitute one full circle.
Shaded portion = (blue square) - (one full circle) = 4 - π.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Brent@GMATPrepNow
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Here's a different approach:Brent@GMATPrepNow wrote:
If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€
Answer: D
Difficulty level: 700+
Source: www.gmatprepnow.com
Let's place a square around just one of the circles
Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
So, let's determine the area of the shaded area in the diagram below.
Each side of the square has length 2, so the area of the SQUARE = (2)(2) = 4
The circle has radius 1.
So, the area of the CIRCLE = π(radius)² = π(1)² = π
So, the area of the SHADED region = 4 - π
Answer: D
Cheers,
Brent
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