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In the figure above, a circular pond is bordered by a garden with a un
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17 Jan 2019, 04:30
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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:
20190117_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
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17 Jan 2019, 05:16
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: 20190117_1528.png Given, Area of pond= 81π Or, radius of pond=9 Area of the shaded region=Total area Area of pond=\(π(9+2)^281π=40π\) Ans. (D)
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Re: In the figure above, a circular pond is bordered by a garden with a un
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17 Jan 2019, 05:21
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 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
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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
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17 Jan 2019, 08:41
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: 20190117_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
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21 Jan 2019, 19:17
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: 20190117_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
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21 Aug 2019, 01:52
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: 20190117_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
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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 121pi81pi = 40 pi
Ans: D




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