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The figure here is a ring with a thickness shown in black. If the radi

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Bunuel
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The figure here is a ring with a thickness shown in black. If the radi [#permalink] New post   25 May 2016, 04:45
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The figure here is a ring with a thickness shown in black. If the radius of the ring is r and the thickness of the ring is t, then which of the following expressions best describes the area of the ring?

(A) π(r-t)2
(B) π(r2-t2)
(C) 2π(r-2t)
(D) πr(2r-t)
(E) πt(2r-t)

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Re: The figure here is a ring with a thickness shown in black. If the radi [#permalink] New post   25 May 2016, 08:29
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This question is vague, Is the inner radius, r or the outer radius ? GMAT being for global students, would certainly avoid such vagueness. Could you tell where this question is from ?
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Re: The figure here is a ring with a thickness shown in black. If the radi [#permalink] New post   25 May 2016, 09:04
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Area of circle with ring - π(r^2)
Thickness of ring is t so area of circle without outer ring - π(r-t)^2
Area of ring = Area of circle with ring - Are of circle without outer ring
or
πr^2 - π(r-t)^2
π(r^2 - r^2 - t^2 + 2*r*t) = πt(2r-t)
Answer is : E
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The figure here is a ring with a thickness shown in black. If the radi [#permalink] New post   17 Jun 2017, 19:57
Bunuel wrote:

The figure here is a ring with a thickness shown in black. If the radius of the ring is r and the thickness of the ring is t, then which of the following expressions best describes the area of the ring?

(A) π(r-t)2
(B) π(r2-t2)
(C) 2π(r-2t)
(D) πr(2r-t)
(E) πt(2r-t)

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Ring is a Circle with a inner circle and outer circle with a thickness.

Given the radius of Outer circle is \(r\).

Let the radius of the inner circle be \(x\).

Thickness of ring \(t = r - x\)

\(x = r - t\)

Area of ring = Area of outer circle - Area of inner circle.

\(\pi\)\(r^2\) - \(\pi\)\(x^2\)

\(\pi (r^2 - x^2)\)

\(\pi (r + x)(r-x)\) ------------- (Converting \(a^2 - b^2 = (a+b)(a-b)\) format)

\(\pi (r + r - t)(t)\) ------------- (Substituting \(x = r-t\) and \(t = r-x\))

\(\pi t (2r - t)\) . Answer (E)...
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Re: The figure here is a ring with a thickness shown in black. If the radi [#permalink] New post   29 Aug 2023, 03:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The figure here is a ring with a thickness shown in black. If the radi [#permalink]
29 Aug 2023, 03:00
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