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SVP  Joined: 06 Sep 2013
Posts: 1545
Concentration: Finance
The rectangular region above contains two circles and a semi  [#permalink]

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Difficulty:   5% (low)

Question Stats: 88% (02:18) correct 12% (02:45) wrong based on 285 sessions

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Attachment: Untitled.png [ 9.48 KiB | Viewed 5720 times ]
The rectangular region above contains two circles and a semicircle, each with a radius of 7. If 22/7 is used as an approximation for π, then the area of the shaded region is approximately

(A) 105
(B) 210
(C) 380
(D) 385
(E) 405

Originally posted by jlgdr on 11 Oct 2013, 17:25.
Last edited by Bunuel on 11 Oct 2013, 17:52, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 59671
Re: The rectangular region above contains two circles and a semi  [#permalink]

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1 The rectangular region above contains two circles and a semicircle, each with a radius of 7. If 22/7 is used as an approximation for π, then the area of the shaded region is approximately

(A) 105
(B) 210
(C) 380
(D) 385
(E) 405

The dimensions of the rectangle is 5 radii by 2 radii, thus 35 by 14. Therefore its area is 35*14.

The area of the two circles and the semicircle is $$2.5*\pi{r^2}=\frac{5}{2}*\frac{22}{7}*7^2=35*11$$.

Thus the area of the shaded region is approximately 35*14-35*11 = 35(14-11)=35*3=105.

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Re: The rectangular region above contains two circles and a semi  [#permalink]

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jlgdr wrote:
Attachment:
Untitled.png
The rectangular region above contains two circles and a semicircle, each with a radius of 7. If 22/7 is used as an approximation for π, then the area of the shaded region is approximately

(A) 105
(B) 210
(C) 380
(D) 385
(E) 405

Area of 2 Circles = 2*[22/7 * 7 * 7] = 2 * 154 = 308

Area of semicircle = 1/2 * [ 154 ] = 77.

Total Area of 2 circles + Semicircle = 308 + 77 = 385

Area of Rectangle = 35 * 14 = 490

Area of shaded region = 490 - 385 = 105

Option A
Hope it is clear

Cheers
Qoofi
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Re: The rectangular region above contains two circles and a semi  [#permalink]

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Hey, can somebody explain here , why the dimensions of the rectangle are 35 by 14, when we are given only the radius is 7.

Help is appreciated.

Thanks in advance Math Expert V
Joined: 02 Sep 2009
Posts: 59671
Re: The rectangular region above contains two circles and a semi  [#permalink]

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1
dheeraj24 wrote:
Hey, can somebody explain here , why the dimensions of the rectangle are 35 by 14, when we are given only the radius is 7.

Help is appreciated.

Thanks in advance Look at the diagram below:
Attachment: Untitled.png [ 10 KiB | Viewed 4684 times ]
The length of the rectangle is 5r, so 5*7=35 and the width is 2r, so 2*7=14.

Hope it's clear.
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Manager  Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 99
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WE: Information Technology (Computer Software)
Re: The rectangular region above contains two circles and a semi  [#permalink]

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Thanks a lot Bunuel. Bunuel wrote:
dheeraj24 wrote:
Hey, can somebody explain here , why the dimensions of the rectangle are 35 by 14, when we are given only the radius is 7.

Help is appreciated.

Thanks in advance Look at the diagram below:
Attachment:
Untitled.png
The length of the rectangle is 5r, so 5*7=35 and the width is 2r, so 2*7=14.

Hope it's clear.
Non-Human User Joined: 09 Sep 2013
Posts: 13737
Re: The rectangular region above contains two circles and a semi  [#permalink]

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_________________ Re: The rectangular region above contains two circles and a semi   [#permalink] 14 Sep 2018, 14:45
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