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The figure above is partitioned into sectors of circles with radius 4.

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The figure above is partitioned into sectors of circles with radius 4. [#permalink]

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New post 29 Nov 2017, 21:54
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The figure above is partitioned into sectors of circles with radius 4. What is the area of the shaded region?

(A) 16
(B) 24π
(C) 28π
(D) 32π
(E) 40π

[Reveal] Spoiler:
Attachment:
2017-11-30_0949_001.png
2017-11-30_0949_001.png [ 45.74 KiB | Viewed 308 times ]
[Reveal] Spoiler: OA

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Re: The figure above is partitioned into sectors of circles with radius 4. [#permalink]

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New post 29 Nov 2017, 22:00
D. 32.pi

The figure is made up of two full circles of radius 4. Hence area =2*pi*4^2 =32.pi


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Re: The figure above is partitioned into sectors of circles with radius 4. [#permalink]

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New post 30 Nov 2017, 10:37
Bunuel wrote:
Image
The figure above is partitioned into sectors of circles with radius 4. What is the area of the shaded region?

(A) 16
(B) 24π
(C) 28π
(D) 32π
(E) 40π

[Reveal] Spoiler:
Attachment:
2017-11-30_0949_001.png



There are two ways to solve it.

Method 1:



Find the area of the 4 sectors.

Two sectors have angle 90 degrees at the centre and the other two have angle 270 degrees at the centre.

The radius for all the four sectors(r) = 4

Total area = \(2* \frac{90}{360} * π * r^2 + 2* \frac{270}{360} * π * r^2\)
= \(2 * π * 4^2\)
= \(32 π\)

Method 2:



If we visualises properly, we will notice that we have two circles in this diagram.
The radius of the circle = 4
Thus, total area = \(2 * π * r^2 = 32π\)
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Re: The figure above is partitioned into sectors of circles with radius 4. [#permalink]

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New post 02 Dec 2017, 13:59
The figure basically comprises two circles, each circle with radius 4.

So, Total area of shaded portion= 2*(πr^2)= 2*π*16= 32π.

Ans D

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Re: The figure above is partitioned into sectors of circles with radius 4.   [#permalink] 02 Dec 2017, 13:59
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The figure above is partitioned into sectors of circles with radius 4.

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