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If the diameter of circle C is 3 times the diameter of circl

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If the diameter of circle C is 3 times the diameter of circl [#permalink] New post 24 Jan 2017, 07:48
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92% (00:57) correct 7% (04:47) wrong based on 28 sessions


If the diameter of circle C is 3 times the diameter of circle D, then the area of circle C is how many times the area of circle D ?



[Reveal] Spoiler: times greater
9

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Re: If the diameter of circle C is 3 times the diameter of circl [#permalink] New post 28 Jan 2017, 07:43
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Explanation

Supply a number for the diameter of Circle D and then find the radius and diameter of the other circle. We chose d = 2 so that we could have a radius of 1.


Image


Compute the area of each circle:
Circle D: Area = \(\pi r^2\) → \(\pi(1)^2\) → \(1\pi\)
Circle C: Area = \(\pi r^2\) → \(\pi(3)^2\) → \(9\pi\)
The area of Circle C is 9 times as large as the area of Circle D.

Hence 9 is the correct answer.
[Reveal] Spoiler: Image
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di new.jpg
di new.jpg [ 26.99 KiB | Viewed 24692 times ]

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Re: If the diameter of circle C is 3 times the diameter of circl [#permalink] New post 20 Jan 2019, 18:28
1 3
1pi 9pi

9 times
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Re: If the diameter of circle C is 3 times the diameter of circl [#permalink] New post 13 Feb 2019, 13:54
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Carcass wrote:


If the diameter of circle C is 3 times the diameter of circle D, then the area of circle C is how many times the area of circle D ?



[Reveal] Spoiler: times greater
9


I like Sandy's strategy of choosing some numbers that satisfy the information in the question.

That said we can also solve the question using algebra only.

Let r = radius of the SMALL circle
So, 3r = radius of the LARGE circle

Area = π(radius)²


Area of SMALL circle = π(r)² = πr²
Area of LARGE circle = π(3r)² = 9πr²

At this point, we can see that the area of the LARGE circle is 9 times the area of the SMALL circle

Answer: 9

Cheers,
Brent
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Re: If the diameter of circle C is 3 times the diameter of circl   [#permalink] 13 Feb 2019, 13:54
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