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

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

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29 Nov 2017, 22:54
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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 [ 45.74 KiB | Viewed 427 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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29 Nov 2017, 23:00
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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30 Nov 2017, 11:37
Bunuel wrote:

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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02 Dec 2017, 14:59
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, 14:59
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