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Circles of radius 2 and 3 are externally tangent and are circumscribed

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Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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New post 19 Mar 2019, 00:01
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A
B
C
D
E

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Question Stats:

100% (01:06) correct 0% (00:00) wrong based on 13 sessions

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Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.


(A) \(3\pi\)

(B) \(4\pi\)

(C) \(6\pi\)

(D) \(9\pi\)

(E) \(12\pi\)


Attachment:
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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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New post 19 Mar 2019, 00:18

Solution


Given:
    • Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the given diagram.

To find:
    • The area of the shaded region.

Approach and Working:
Diameter of the third (biggest) circle = diameter of first circle + diameter of second circle = 6 + 4 = 10
    • Therefore, radius of the third circle = 5
    • So, area of the shaded region = area of the third circle – (area of first circle + area of second circle) = π(5)2 – [π(2)2 + π(3)2] = 25π – 13π = 12π

Hence, the correct answer is option E.

Answer: E

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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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New post 19 Mar 2019, 02:28
IMO E

Radious of big circle = 5

so area of two small circles = 13π

area of big circele = 25 π

so area of shaded region = 25 π - 13π = 12π

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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed  [#permalink]

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New post 19 Mar 2019, 03:52
[quote="Bunuel"]Image
Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.


(A) \(3\pi\)

(B) \(4\pi\)

(C) \(6\pi\)

(D) \(9\pi\)

(E) \(12\pi\)

large circle radius = 5
area = 25pi
small circle area = 9pi+4pi = 13 pi
shaded region = 25pi-13pi = 12pi
IMO E
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Re: Circles of radius 2 and 3 are externally tangent and are circumscribed   [#permalink] 19 Mar 2019, 03:52
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Circles of radius 2 and 3 are externally tangent and are circumscribed

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