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A circular lawn with a radius of 5 meters is surrounded by a circular

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A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post Updated on: 06 Oct 2018, 02:19
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A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

A. 81 π
B. 56 π
C. 25 π
D. 20 π
E. cannot be determined

To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose

Originally posted by josemnz83 on 22 Jun 2013, 06:35.
Last edited by Bunuel on 06 Oct 2018, 02:19, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 22 Jun 2013, 08:14
josemnz83 wrote:
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose


There is a figure attached to the original question. See below:
Attachment:
Circle.png
Circle.png [ 6.23 KiB | Viewed 8867 times ]
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide (see figure). What is the area of the walkway?

Hope it heps.
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 22 Jun 2013, 08:36
Thanks Bunuel. I have each of the Manhattan guides so I had seen the figure before. I did not post it because I did not want to violate posting rules. Anyway even after looking at the figure I cannot understand why the radius of the walkway is not 2. Radius is half of the diameter. The problem says that the walkway is 4 meters wide. Is 4 meters not the diameter? Or is the radius 4 because the walkway is not really a "full circle" but more like a semicircle of sorts?

Thanks!

Bunuel wrote:
josemnz83 wrote:
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose


There is a figure attached to the original question. See below:
Attachment:
Circle.png
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide (see figure). What is the area of the walkway?

Hope it heps.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 22 Jun 2013, 08:41
1
josemnz83 wrote:
Thanks Bunuel. I have each of the Manhattan guides so I had seen the figure before. I did not post it because I did not want to violate posting rules. Anyway even after looking at the figure I cannot understand why the radius of the walkway is not 2. Radius is half of the diameter. The problem says that the walkway is 4 meters wide. Is 4 meters not the diameter? Or is the radius 4 because the walkway is not really a "full circle" but more like a semicircle of sorts?

Thanks!

Bunuel wrote:
josemnz83 wrote:
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose


There is a figure attached to the original question. See below:
Attachment:
The attachment Circle.png is no longer available
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide (see figure). What is the area of the walkway?

Hope it heps.


Attachment:
Untitled.png
Untitled.png [ 6.82 KiB | Viewed 7061 times ]

Circular lawn = green area;
Walkaway = yellow area.

Does this make sense?
_________________

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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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 22 Jun 2013, 08:48
josemnz83 wrote:
Image
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?



To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose


Area of smaller circle = 5pie

Now how would you calculate area of walkway= Area of smaller circle- area of bigger circle(includes walkway)
= 5- (5+4) = 5-9= 4
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 22 Jun 2013, 08:55
Thanks for the help! I feel really dumb right now. lol

What I failed to recognize is that the 4 was indicating half of the walkway outside of the circular lawn. The diameter of the whole circle was 18 (10 for the lawn + 4 for one "side" of the walkway" + 4 for other side). Radius then would be 9 pi. The rest I did not have trouble with.

Thanks so much for the prompt replies!

prateekbhatt wrote:
josemnz83 wrote:
Image
A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?



To figure out the area of the walkway I found the difference between of the larger circle (circular lawn + circular walkway). To find the radius of the bigger circle I added the diameter of both the circular walkway and the circular lawn and divided by 2. (10+4)/2. I found the radius of the circle to be 7. So area of the bigger circle would be (7)squared times pi.

The Manhattan guide explains that the area of the bigger circle is 9(squared) times pie. Why is the radius of the bigger circle 9? I understand that the radius of the smaller circle is 5 but wouldn't the radius of the circular walkway be 2 since the entire walkway is 4 meters wide?

Please help!

Jose


Area of smaller circle = 5pie

Now how would you calculate area of walkway= Area of smaller circle- area of bigger circle(includes walkway)
= 5- (5+4) = 5-9= 4
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 10 Oct 2013, 19:37
2
Radius of larger circle (Walk area inclusive) = 5 +4 =9
Area = Pie (9) ^2 = 81pie......................... (1)

Radius of smaller circle = 5
Area = Pie (5) ^2 = 25pie.......................... (2)

Area of walkway = (1) - (2) = 56pie
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 18 Nov 2013, 18:11
\(pi(R^2-r^2)\).
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular  [#permalink]

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New post 07 Oct 2018, 21:52
Area of the smaller circle = πr^2 = π x5^2 = 25π
Area of the larger circle = πr^2 = π x 9^2 = 81π
Difference(Area of the walkway) = 81π - 25π = 56π

Hence B
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Re: A circular lawn with a radius of 5 meters is surrounded by a circular &nbs [#permalink] 07 Oct 2018, 21:52
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