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The figure above shows a circular flower bed, with its cente

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Walkabout
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The figure above shows a circular flower bed, with its cente [#permalink] New post   20 Dec 2012, 06:43
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The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) \(25\pi\)
(B) \(38\pi\)
(C) \(55\pi\)
(D) \(57\pi\)
(E) \(64\pi\)


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Re: The figure above shows a circular flower bed, with its cente [#permalink] New post   20 Dec 2012, 06:48
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The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) \(25\pi\)
(B) \(38\pi\)
(C) \(55\pi\)
(D) \(57\pi\)
(E) \(64\pi\)

The radius of the bigger circle is 8 + 3 = 11 feet, thus its area is \(\pi{r^2}=121\pi\).

The area of the smaller circle is \(\pi{8^2}=64\pi\).

The difference is \(121\pi-64\pi=57\pi\).

Answer: D.
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Re: The figure above shows a circular flower bed, with its cente [#permalink] New post   26 Apr 2016, 15:15
\(Radius of total garden\) = 8 + 3 = 11 \(feet\)
\(Area of flower bed including path\) = \(\pi\)\(11^2\)
\(Area of flower bed\) = \(\pi\) \(8^2\)
\(Area of only path\) = 57\(\pi\) sq.feet
\(correct answer\) - D
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Re: The figure above shows a circular flower bed, with its cente [#permalink] New post   Updated on: 19 Apr 2020, 12:21
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Walkabout wrote:
Attachment:
Circle.png
The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) \(25\pi\)
(B) \(38\pi\)
(C) \(55\pi\)
(D) \(57\pi\)
(E) \(64\pi\)


The circular path (i.e., the shaded region) is called an annulus in geometry. Basically an annulus is a ring-shaped figure bounded by two concentric circles. To find the area of an annulus, we use the following formula:

π(R^2 – r^2)

where r is the radius of the inner circle and R is the radius of the outer circle.

We know:

R = 8 + 3 = 11 feet

r = 8 feet

Plugging into our equation, we have:

area = π(11^2 – 8^2)

area = π(121 - 64)

area = 57π

Answer: D

Originally posted by JeffTargetTestPrep on 27 Apr 2016, 08:44.
Last edited by JeffTargetTestPrep on 19 Apr 2020, 12:21, edited 1 time in total.
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Re: The figure above shows a circular flower bed, with its cente [#permalink] New post   05 Jul 2016, 06:16
Walkabout wrote:
Attachment:
Circle.png
The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) \(25\pi\)
(B) \(38\pi\)
(C) \(55\pi\)
(D) \(57\pi\)
(E) \(64\pi\)








8+3=11
11^2=121

8^2= 64


121pi -64 pi= 57 pi
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Re: The figure above shows a circular flower bed, with its center at O, su [#permalink] New post   01 Dec 2017, 08:21
Area of the path = Area of larger circle (with radius 8+3=11) - Area of smaller circle (with radius 8)
=>Area of the path = π∗(11)^2 - π∗(8)^2
=>Area of the path = 121π - 64π = 57π
Answer: D
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Re: The figure above shows a circular flower bed, with its cente [#permalink] New post   01 Oct 2023, 01:00
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Re: The figure above shows a circular flower bed, with its cente [#permalink]
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