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The rectangular region above contains two circles and a semi

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

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New post Updated on: 11 Oct 2013, 17:52
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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.
Added the figure.
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Re: The rectangular region above contains two circles and a semi  [#permalink]

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New post 11 Oct 2013, 17:56
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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.

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

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New post 11 Oct 2013, 20:31
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

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

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New post 14 Apr 2014, 00:34
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 :)
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Re: The rectangular region above contains two circles and a semi  [#permalink]

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New post 14 Apr 2014, 01:25
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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
Untitled.png [ 10 KiB | Viewed 4050 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 14 Apr 2014, 01:57
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.
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Re: The rectangular region above contains two circles and a semi  [#permalink]

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New post 14 Sep 2018, 14:45
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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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