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# The figure above shows a circular flower bed, with its center at O, su

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Math Expert
Joined: 02 Sep 2009
Posts: 45498
The figure above shows a circular flower bed, with its center at O, su [#permalink]

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28 Nov 2017, 21:04
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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) 25π
(B) 38π
(C) 55π
(D) 57π
(E) 64π

Attachment:

2017-11-28_1025.png [ 6.37 KiB | Viewed 471 times ]

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The figure above shows a circular flower bed, with its center at O, su [#permalink]

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28 Nov 2017, 21:16
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KUDOS

The outer circle has the radius of 8+3(since the circular path around the flower bed is 3 feet) = 11
Hence, the area of the outer circle is $$π*(11)^2 = 121π$$
Since the radius of the inner circle is 8, area will be $$π*(8)^2 = 64π$$

The area of the path will be the difference of area of the outer circle and the area of the inner circle.
Hence area of the path will be $$121π - 64π = 57π$$(Option D)
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Re: The figure above shows a circular flower bed, with its center at O, su [#permalink]

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01 Dec 2017, 07:56
Bunuel wrote:

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) 25π
(B) 38π
(C) 55π
(D) 57π
(E) 64π

Attachment:
2017-11-28_1025.png

The area of the inner circle is 8^2π = 64π.

The area of the outer circle is 11^2π = 121π.

Thus, the area of the path is the difference of the two areas: 121π - 64π = 57π.

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Re: The figure above shows a circular flower bed, with its center at O, su [#permalink]

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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
Re: The figure above shows a circular flower bed, with its center at O, su   [#permalink] 01 Dec 2017, 08:21
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