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# The diameters of the semicircles above are 8, and the diameter of the

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
The diameters of the semicircles above are 8, and the diameter of the  [#permalink]

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30 Oct 2018, 02:44
00:00

Difficulty:

15% (low)

Question Stats:

86% (02:17) correct 14% (02:09) wrong based on 34 sessions

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The diameters of the semicircles above are 8, and the diameter of the semicircle on the right is perpendicular to those of the other two semicircles. What is the total area of the shaded region?

A. 12π + 64
B. 24π + 12
C. 24π + 48
D. 32π + 48
E. 32π + 64

Attachment:

cird06.png [ 12.2 KiB | Viewed 433 times ]

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Joined: 24 Jun 2013
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Location: India
Schools: ISB '20, GMBA '20
Re: The diameters of the semicircles above are 8, and the diameter of the  [#permalink]

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30 Oct 2018, 11:01
Bunuel wrote:

The diameters of the semicircles above are 8, and the diameter of the semicircle on the right is perpendicular to those of the other two semicircles. What is the total area of the shaded region?

A. 12π + 64
B. 24π + 12
C. 24π + 48
D. 32π + 48
E. 32π + 64

Attachment:
cird06.png

Area of 1 semicircle =$$\frac{π r^2}{2}$$ = 8π , 3 semicircles so total area of 3 semicircles = 3 x 8π = 24π

Also since diameter are same we would get a square figure at the centre (sides equal and perpendicular) , so are one bigger triangle = $$\frac{8*8}{2}$$= 32 , now smaller triangle is half of this area so smaller traingle = 16, likewise we have 3 smaller triangle so area = 48

total area 24π + 48
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Re: The diameters of the semicircles above are 8, and the diameter of the   [#permalink] 30 Oct 2018, 11:01
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