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# The figure above shows a circular garden plot with center O surrounded

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Math Expert
Joined: 02 Sep 2009
Posts: 51263
The figure above shows a circular garden plot with center O surrounded  [#permalink]

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26 Jun 2018, 04:13
00:00

Difficulty:

25% (medium)

Question Stats:

88% (01:11) correct 12% (01:38) wrong based on 33 sessions

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The figure above shows a circular garden plot with center O surrounded by a circular sidewalk, also with center O. If the area covered by the garden and sidewalk together is $$169\pi$$ and of the garden alone is $$144\pi$$, what is the value of T ?

A) 1

B) 2

C) 3

D 5

E) 12.5

Attachment:

mHNyYFH.jpg [ 14.69 KiB | Viewed 424 times ]

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Re: The figure above shows a circular garden plot with center O surrounded  [#permalink]

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26 Jun 2018, 05:39

Solution

Given:
• Area covered by the garden and sidewalk together is 169π
• Area covered by the garden alone is 144π

To find:
• The value of T

Approach and Working:
If we assume the radius of the circle to be r, then we can write
• $$Π r^2 = 144 Π$$
Or, r = 12

As the combined area of the garden and the sidewalk is 169 Π, we can write
• $$Π (r + T)^2 = 169 Π$$
Or, $$(12 + T)^2 = 13^2$$
Or, 12 + T = 13
Or, T = 1

Hence, the correct answer is option A.

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Re: The figure above shows a circular garden plot with center O surrounded  [#permalink]

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26 Jun 2018, 09:16
My take - Area covered by the garden and sidewalk together is 169π. Area = πr2 . so r =13 from second equation rr=12t . T=13 -12 =1

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The figure above shows a circular garden plot with center O surrounded  [#permalink]

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26 Jun 2018, 09:29
Outer circle -> $$169\pi$$=$$\pi r^2$$ -> r = 13
Inner circle -> $$144\pi$$=$$\pi r^2$$ -> r = 12

Subtract both: 13 - 12 = 1

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Re: The figure above shows a circular garden plot with center O surrounded  [#permalink]

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26 Jun 2018, 10:01
Bunuel wrote:

The figure above shows a circular garden plot with center O surrounded by a circular sidewalk, also with center O. If the area covered by the garden and sidewalk together is $$169\pi$$ and of the garden alone is $$144\pi$$, what is the value of T ?

A) 1

B) 2

C) 3

D 5

E) 12.5

Attachment:
mHNyYFH.jpg

$$Area \ of \ T = πR^2 - πr^2$$

So, $$169\pi$$ $$-$$ $$144\pi$$ = $$πR^2 - πr^2$$

Or, $$25π$$ $$=$$ $$π(R^2 - r^2)$$

Or, $$25 = (R + r)(R - r)$$

So, $$R = 3$$ and $$r = 2$$

Hence, T is $$3 - 2$$ = $$1$$, Answer must be (A)
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Abhishek....

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Re: The figure above shows a circular garden plot with center O surrounded &nbs [#permalink] 26 Jun 2018, 10:01
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