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# If the radius of the circle H in the figure above is 2/3 of the radius

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Joined: 02 Sep 2009
Posts: 50007
If the radius of the circle H in the figure above is 2/3 of the radius  [#permalink]

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13 Nov 2017, 08:12
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Difficulty:

35% (medium)

Question Stats:

76% (02:55) correct 24% (02:06) wrong based on 24 sessions

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If the radius of the circle H in the figure above is 2/3 of the radius of the circle G, and the radius of circle G is 3/4 of the radius of the circle F, then the area of the shaded region is what part of the area of circle F?

(A) 1/12
(B) 17/144
(C) 1/4
(D) 5/16
(E) 9/16

Attachment:

2017-11-13_1910.png [ 9.94 KiB | Viewed 676 times ]

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Re: If the radius of the circle H in the figure above is 2/3 of the radius  [#permalink]

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13 Nov 2017, 08:39
Bunuel wrote:

If the radius of the circle H in the figure above is 2/3 of the radius of the circle G, and the radius of circle G is 3/4 of the radius of the circle F, then the area of the shaded region is what part of the area of circle F?

(A) 1/12
(B) 17/144
(C) 1/4
(D) 5/16
(E) 9/16

Attachment:
2017-11-13_1910.png

Let the radius of circle F be x; radius of circle G will be 3x/4; radius of circle H will be x/2
Area of shaded region is 9x^2/16 - x^2/4 = 5x^2/16 (pie)
Shaded region part is 5/16 part of area of circle F
D
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If the radius of the circle H in the figure above is 2/3 of the radius  [#permalink]

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13 Nov 2017, 08:43
Bunuel wrote:

If the radius of the circle H in the figure above is 2/3 of the radius of the circle G, and the radius of circle G is 3/4 of the radius of the circle F, then the area of the shaded region is what part of the area of circle F?

(A) 1/12
(B) 17/144
(C) 1/4
(D) 5/16
(E) 9/16

Attachment:
2017-11-13_1910.png

let the radius of circle F be $$12$$

so radius of circle G $$=12*\frac{3}{4}=9$$ and radius of circle H $$= 9*\frac{2}{3}=6$$

Area of shaded region = Area of circle G-Area of circle H$$= π9^2-π6^2 = 45π$$

Area of circle F $$= π12^2=144π$$

Area of shaded region to area of circle F $$= \frac{45π}{144π}=\frac{5}{16}$$

Option D
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If the radius of the circle H in the figure above is 2/3 of the radius  [#permalink]

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13 Nov 2017, 10:58
Bunuel wrote:

If the radius of the circle H in the figure above is 2/3 of the radius of the circle G, and the radius of circle G is 3/4 of the radius of the circle F, then the area of the shaded region is what part of the area of circle F?

(A) 1/12
(B) 17/144
(C) 1/4
(D) 5/16
(E) 9/16

Attachment:
2017-11-13_1910.png

Radii for H, G, and F:

$$H = \frac{2}{3}G$$
$$\frac{H}{G}=\frac{2}{3}$$
$$H = 2, G = 3$$

$$G = \frac{3}{4}F$$
$$3=\frac{3}{4}F$$
$$F = 4$$

Area of H = $$\pi*r^2= 4\pi$$
Area of G = $$9\pi$$
Area of F = $$16\pi$$

Shaded region's area = (Area of G) - (Area of H)
$$(9\pi - 4\pi) = 5\pi$$

Area of the shaded region is what part of the area of circle F?
$$\frac{5\pi}{16\pi}=\frac{5}{16}$$

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If the radius of the circle H in the figure above is 2/3 of the radius &nbs [#permalink] 13 Nov 2017, 10:58
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