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Re: If each of the 4 circles above has radius 1, [#permalink]
GreenlightTestPrep wrote:
Image

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 – 2π


Here's a different approach:

Let's place a square around just one of the circles
Image


Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
Image


This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
Image


So, let's determine the area of the shaded area in the diagram below.
Image

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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Re: If each of the 4 circles above has radius 1, [#permalink]
1
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
Image

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 – 2π


Here's a different approach:

Let's place a square around just one of the circles
Image


Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
Image


This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
Image


So, let's determine the area of the shaded area in the diagram below.
Image

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

This approach would save some time

Posted from my mobile device Image
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Re: If each of the 4 circles above has radius 1, [#permalink]
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