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In the figure above, a circular pond is bordered by a garden with a un

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In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 17 Jan 2019, 04:30
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A
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C
D
E

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Question Stats:

93% (01:23) correct 7% (01:45) wrong based on 44 sessions

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In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π

Attachment:
2019-01-17_1528.png
2019-01-17_1528.png [ 12.64 KiB | Viewed 745 times ]

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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 17 Jan 2019, 05:16
Bunuel wrote:
Image
In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π

Attachment:
2019-01-17_1528.png


Given, Area of pond= 81π Or, radius of pond=9

Area of the shaded region=Total area- Area of pond=\(π(9+2)^2-81π=40π\)
Ans. (D)
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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 17 Jan 2019, 05:21
Bunuel wrote:
Image
In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π


Area of shaded region = Area of bordered circle - Area of pond

Area of pond = 81π
radius = 9

Area of bordered circle = 121π ( π 11^2)

Area of shaded region = 121π - 81π
Area of shaded region = 40π

Answer D
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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 17 Jan 2019, 06:55

Solution


Given:
    • A circular pond is bordered by a garden with a uniform width of 2
    • Area of pond = 81ᴨ

To find:
    • Area of the shaded region

Approach and Working:
    • Area of shaded region = area of bigger circle – area of pond

Radius of bigger circle = radius of pond + width of the garden
    • Radius of pond = √81 = 9
    • Thus, radius of bigger circle = 9 + 2 = 11

Therefore, area of shaded region = \(ᴨ(11^2 – 9^2) = 40ᴨ\)

Hence, the correct answer is Option D

Answer: D

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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 17 Jan 2019, 08:41
Bunuel wrote:
Image
In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π

Attachment:
2019-01-17_1528.png


area of pond = pi * r 2 = 81 pi ; r = 9
so garden + pond = 9+2 = 11 ; area = 121 pi
area of shaded region = 121pi -81pi = 40 pi
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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 21 Jan 2019, 19:17
Bunuel wrote:
Image
In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π

Attachment:
2019-01-17_1528.png


Since the area of the pond is 81π, the radius of the pond is 9, and thus the radius of the entire figure (pond plus garden) is 11.

Thus, the area of the shaded region is:

π(11^2) - π(9^2) = π(11^2 - 9^2) = π(121 - 81) = 40π

Answer: D
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Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 21 Aug 2019, 01:52
Bunuel wrote:
Image
In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region. If the area of the circular pond is 81π, what is the area of the shaded region?

A 16π
B 20π
C 36π
D 40π
E 169π

Attachment:
2019-01-17_1528.png


Given:
1. In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region.
2. The area of the circular pond is 81π.

Asked: What is the area of the shaded region?

2. The area of the circular pond is 81π.
Radius of the circular pond is 9.

1. In the figure above, a circular pond is bordered by a garden with a uniform width of 2, represented by the shaded region.
Radius of pond + garden = 11

The area of the shaded region = \(\pi (R^2 - r^2) = \pi (11^2 - 9^2) = \pi (121 - 81) = 40\pi\)

IMO D
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In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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New post 21 Aug 2019, 02:00
Directly jumping into the question tells me that to find out the area of the shaded region.

Area of the shaded region is given by = Outer circle - Inner Circle

Inner Circle Area is 81pi, we need to find out the outer circle radius. Thus, Outer Circle radius is Inner Circle radius + 2 (which is given in the question)

Inner Circle radius is 9 (the area is given as 81pi. So, the radius can be found by applying the Area of the Circle formula - pi(radius)^2)
So, Outer Circle radius is 9+2 = 11

Area of Shaded Region is 121pi-81pi = 40 pi

Ans: D
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In the figure above, a circular pond is bordered by a garden with a un   [#permalink] 21 Aug 2019, 02:00
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