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

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Joined: 02 Sep 2009
Posts: 52285
What is the area of the shaded portion of the figure above?  [#permalink]

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01 Feb 2018, 22:45
00:00

Difficulty:

15% (low)

Question Stats:

85% (00:45) correct 15% (00:34) wrong based on 57 sessions

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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 [ 20.46 KiB | Viewed 1932 times ]

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

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01 Feb 2018, 22:48
1
Bunuel wrote:

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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02 Feb 2018, 04:44
1
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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02 Feb 2018, 06:19
Bunuel wrote:

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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02 Feb 2018, 09:36
Bunuel wrote:

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) - (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: $$8 - 2\pi$$

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

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05 Feb 2018, 09:17
Bunuel wrote:

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.

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Re: What is the area of the shaded portion of the figure above? &nbs [#permalink] 05 Feb 2018, 09:17
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# What is the area of the shaded portion of the figure above?

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