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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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17 Jan 2019, 03:30
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Difficulty:

5% (low)

Question Stats:

93% (01:10) correct 7% (01:42) wrong based on 42 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 [ 12.64 KiB | Viewed 413 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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17 Jan 2019, 04:16
Bunuel wrote:

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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17 Jan 2019, 04:21
Bunuel wrote:

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

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

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

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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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17 Jan 2019, 05:55

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

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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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17 Jan 2019, 07:41
Bunuel wrote:

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
IMO 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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21 Jan 2019, 18:17
Bunuel wrote:

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

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Re: In the figure above, a circular pond is bordered by a garden with a un   [#permalink] 21 Jan 2019, 18:17
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