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Math Expert V
Joined: 02 Sep 2009
Posts: 58428
In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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Difficulty:   5% (low)

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

HideShow timer Statistics 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 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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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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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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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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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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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]

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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:
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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Joined: 07 May 2016
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In the figure above, a circular pond is bordered by a garden with a un  [#permalink]

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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 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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