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What is the area of the shaded portion of the figure above?

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What is the area of the shaded portion of the figure above?  [#permalink]

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New post 01 Feb 2018, 23:45
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What is the area of the shaded portion of the figure above?

(A) \(8 -8\pi\)

(B) \(8 -4\pi\)

(C) \(8 -2\pi\)

(D) \(8 -\pi\)

(E) \(\pi\)

Attachment:
2018-02-02_1042.png
2018-02-02_1042.png [ 20.46 KiB | Viewed 1587 times ]

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Re: What is the area of the shaded portion of the figure above?  [#permalink]

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New post 01 Feb 2018, 23:48
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Bunuel wrote:
Image
What is the area of the shaded portion of the figure above?

(A) \(8 -8\pi\)

(B) \(8 -4\pi\)

(C) \(8 -2\pi\)

(D) \(8 -\pi\)

(E) \(\pi\)

Attachment:
2018-02-02_1042.png



Area of rectangle = 8
Area one circle => pie 2^2/4 => pie
Area 2 circles = 2 pie

shaded area = 8 - 2pie

option C
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Re: What is the area of the shaded portion of the figure above?  [#permalink]

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New post 02 Feb 2018, 05:44
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Diameter for circle is 2 so radius =1
Area of rectangle = 4×2 =8
Area of one circle = pi × r^2---> pi so area of two circles = 2 pi
Hence area of shaded region= 8-2pi

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Re: What is the area of the shaded portion of the figure above?  [#permalink]

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New post 02 Feb 2018, 07:19
Bunuel wrote:
Image
What is the area of the shaded portion of the figure above?

(A) \(8 -8\pi\)

(B) \(8 -4\pi\)

(C) \(8 -2\pi\)

(D) \(8 -\pi\)

(E) \(\pi\)

Attachment:
2018-02-02_1042.png

Area of the shaded region is \(4*2 - 2*π*1^2\) = \(8 -2\pi\), Answer will be (C)
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What is the area of the shaded portion of the figure above?  [#permalink]

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New post 02 Feb 2018, 10:36
Bunuel wrote:
Image
What is the area of the shaded portion of the figure above?

(A) \(8 -8\pi\)

(B) \(8 -4\pi\)

(C) \(8 -2\pi\)

(D) \(8 -\pi\)

(E) \(\pi\)

Attachment:
2018-02-02_1042.png

Shaded area =
(Area of rectangle) - (Area of 2 circles)

Area of rectangle = L*W = 8

Area of one circle
--from width = 2, derive radius
--the circle, inscribed in the rectangle, has a diameter equal to width of rectangle
-- d = w = 2
-- d = 2r, 2 = 2r, r = 1
One circle's area = \(\pi r^2 = 1\pi\)
Total area of circles: \(2\pi\)

Shaded region's area: \(8 - 2\pi\)

Answer C
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Re: What is the area of the shaded portion of the figure above?  [#permalink]

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New post 05 Feb 2018, 10:17
Bunuel wrote:
Image
What is the area of the shaded portion of the figure above?

(A) \(8 -8\pi\)

(B) \(8 -4\pi\)

(C) \(8 -2\pi\)

(D) \(8 -\pi\)

(E) \(\pi\)

Attachment:
2018-02-02_1042.png


The diameter of each circle is 2, so the radius of each circle is 1.

Thus, the combined area of the two circles is 2 x π x 1^2 = 2π.

The area of the rectangle is 4 x 2 = 8.

Therefore, the area of the shaded portion is 8 - 2π.

Answer: C
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Re: What is the area of the shaded portion of the figure above? &nbs [#permalink] 05 Feb 2018, 10:17
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