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# Two circles with radii r and r + 2 have areas that differ by 8π. What

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Math Expert
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Two circles with radii r and r + 2 have areas that differ by 8π. What [#permalink]

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27 Nov 2017, 23:33
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Two circles with radii r and r + 2 have areas that differ by 8π. What is the radius of the larger circle?

(A) 1
(B) 2
(C) 3
(D) 8
(E) 9
[Reveal] Spoiler: OA

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Re: Two circles with radii r and r + 2 have areas that differ by 8π. What [#permalink]

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28 Nov 2017, 00:10
C

Area of larger circle = pi.(r+2)^2
Area of smaller circle =pi.r^2

Difference is pi.((r+2)^2-r^2)=8.pi

Solving we get r=1. Hence radius of larger circle =3

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Re: Two circles with radii r and r + 2 have areas that differ by 8π. What [#permalink]

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28 Nov 2017, 15:08
Bunuel wrote:
Two circles with radii r and r + 2 have areas that differ by 8π. What is the radius of the larger circle?

(A) 1
(B) 2
(C) 3
(D) 8
(E) 9

Two circles with radii r and (r + 2) have areas that differ by 8π:

$$π(r+2)^2 - (πr^2) = 8π$$

$$π(r^2 + 4r + 4) - πr^2 = 8π$$

$$πr^2 + 4πr + 4π - πr^2 = 8π$$
$$4πr + 4π = 8π$$
$$4πr = 4π$$
$$r = 1$$

Radius of larger circle = $$(r + 2) = 3$$

Check: Circle 1 area = $$π(1)^2 = π$$. Circle 2 area = $$π(3)^2 = 9π$$. Difference:$$(9π-1π)=8π$$
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Re: Two circles with radii r and r + 2 have areas that differ by 8π. What [#permalink]

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29 Nov 2017, 18:18
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Expert's post
Bunuel wrote:
Two circles with radii r and r + 2 have areas that differ by 8π. What is the radius of the larger circle?

(A) 1
(B) 2
(C) 3
(D) 8
(E) 9

The area of the smaller circle is πr^2.

The area of the larger circle is π(r + 2)^2 = π(r^2 + 4r + 4).

Since the areas differ by 8π, we have:

π(r^2 + 4r + 4) - πr^2 = 8π

r^2 + 4r + 4 - r^2 = 8

4r + 4 = 8

4r = 4

r = 1

Thus, the radius of the larger circle is 1 + 2 = 3.

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Re: Two circles with radii r and r + 2 have areas that differ by 8π. What [#permalink]

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09 Dec 2017, 01:35

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Re: Two circles with radii r and r + 2 have areas that differ by 8π. What   [#permalink] 09 Dec 2017, 01:35
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