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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]  24 Jan 2017, 07:48
Expert's post
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Question Stats:

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]  28 Jan 2017, 07:43
1
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Expert's post
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.

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
Attachment:

di new.jpg [ 26.99 KiB | Viewed 24692 times ]

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Sandy
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Re: If the diameter of circle C is 3 times the diameter of circl [#permalink]  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]  13 Feb 2019, 13:54
1
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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 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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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