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555-605 (Medium)|   Geometry|      
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In the figure above, the centers of four equal circles lie along the 02 Feb 2016, 01:57
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70% (01:32) correct 30% (01:25) wrong based on 106 sessions

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In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

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2016-01-31_1804.png
2016-01-31_1804.png [ 4.24 KiB | Viewed 4084 times ]
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E
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In the figure above, the centers of four equal circles lie along the 02 Feb 2016, 03:26
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Bunuel
In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π
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Hi Bunuel,
The figure has not got attached
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In the figure above, the centers of four equal circles lie along the 02 Feb 2016, 04:16
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chetan2u
Bunuel
In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

Hi Bunuel,
The figure has not got attached
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Added the figure. Thank you.
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In the figure above, the centers of four equal circles lie along the 02 Feb 2016, 04:41
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Bunuel

In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

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Attachment:
2016-01-31_1804.png
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Circumference as 64 pi gives us the diameter as 64..
four equal circles will have dia of 64/4 each = 16...
area of each circle= pi 8^2= 64 pi..
so area of four of them = 64*4=256 pi..
E
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In the figure above, the centers of four equal circles lie along the 02 Feb 2016, 04:42
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Hi Bunnel,

The circumference 2*pi*r=64*pi => r =32 and d=64

4 smaller circles diameter= 64/4= 16 and hence r= 8 for individual smaller circles. Area=pi*r*r = 64*pi . Total area of shaded region = 64*pi*4 = 256*pi

Answer: E
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In the figure above, the centers of four equal circles lie along the Updated on: 04 Feb 2016, 23:45
Originally posted by TeamGMATIFY on 04 Feb 2016, 03:56.
Last edited by TeamGMATIFY on 04 Feb 2016, 23:45, edited 1 time in total.
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Bunuel

In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

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Attachment:
2016-01-31_1804.png
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To find out the area of the shaded regions, first identify the participating figures and their areas.
Here area of the shaded region = sum of area of 4 small circles

Given: Circumference of the large circle = = 2π*r = 64π
Hence radius = 32

There are 2 smaller circles on the radius of the bigger circle.
Therefore 2*diameter of smaller circles = radius of bigger circle = 32
Diameter of smaller circle = 16
radius of smaller circle = 8

Required area = 4* (π*8^2) = 4*64π = 256π
Option E
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In the figure above, the centers of four equal circles lie along the 04 Feb 2016, 21:48
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Bunuel

In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

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Attachment:
2016-01-31_1804.png
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Area of the shaded region = Sum of areas of 4 smaller circles

Circumference of large circle = 64π = πD
i.e. Diameter, D = 64
So diameter of each of Smaller circle = 64/4 = 16
Radius of each of the smaller circle = 16/2=8
Area of shaded region = 4*πr^2 = 4*64π = 256π

Answer: Option E
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In the figure above, the centers of four equal circles lie along the 27 Oct 2020, 16:42
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Circumference of a circle = 2πr = 64π

Therefore r = 32. D = 64.

Area of shaded portion = sum of area of individual circles.
We got the diameter of big circle as 64.

64/4 = 16 = Diameter of individual circles
r = 8

Therefore, area of 1 circle = π\(r^2\) = π*\(8^2\) = 64π

Area of 4 circle = 64π * 4 = 256π

Answer E
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In the figure above, the centers of four equal circles lie along the 31 Oct 2020, 13:49
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Bunuel

In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?

A. 16π
B. 32π
C. 64π
D. 128π
E. 256π

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Solution:

Since the circumference of the large circle is C = π x d = 64π, its diameter is 64π/π = 64. Therefore, the diameter of each smaller circle is 64/4 = 16, and hence the radius of each smaller circle is 8. The area of each smaller circle is therefore A = r^2 xπ = 8^2 x π = 64π, and the area of the shaded region (i.e., the total area of the 4 smaller circles) is 64π x 4 = 256π.

Answer: E
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