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605-655 (Medium)|   Geometry|      
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Bunuel
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If each curved portion of the boundary of the figure attached is forme 18 Aug 2015, 09:19
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45% (medium)

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63% (01:39) correct 37% (02:09) wrong based on 270 sessions

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If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)

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Attachment:
Kaplan.png
Kaplan.png [ 8.21 KiB | Viewed 6982 times ]
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B
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If each curved portion of the boundary of the figure attached is forme 18 Aug 2015, 10:21
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Bunuel

If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)

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Attachment:
Kaplan.png
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The rectangle created by the 2 parallel lines is of dimensions 4X8 = 32 units^2

The 4 semicircular regions will provide a net = 0 impact on the total area of the figure. Thus the total area of the figure = 32 \(\pm\)0 = 32. B is the correct answer.
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If each curved portion of the boundary of the figure attached is forme 18 Aug 2015, 21:16
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Bunuel

If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)

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The attachment Kaplan.png is no longer available
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IMO : B =32

Shaded figure looks like a rectangle with 2 Semicircles added and 2 semicircles removed.
Now those 2 added semicircles will cancel out with the removed semicircles. Check out the below figure
Attachment:
11.jpg
11.jpg [ 14.06 KiB | Viewed 6220 times ]

The area of the shaded region is nothing but the area of the rectangle with sides 4 and 8.
Area = 8*4 =32
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If each curved portion of the boundary of the figure attached is forme 18 Aug 2015, 21:42
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Bunuel
If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)
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Ans: B
Solution: If we shift these semicircle, which are out ward dense, to the blank space of the same size in between parallel lines we will get one big rectangle. so practically we need to find the area of the rectangle only.

which is 8x4= 32 [Ans]
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If each curved portion of the boundary of the figure attached is forme 27 Feb 2016, 01:20
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i thought the figure will form a rectangle when we stretch the sheet
But length will be 4 and breath will be combined circumference of two circle=2pir=4pi.
Please explain again with diagram.
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If each curved portion of the boundary of the figure attached is forme 27 Feb 2016, 05:38
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mahakmalik
i thought the figure will form a rectangle when we stretch the sheet
But length will be 4 and breath will be combined circumference of two circle=2pir=4pi.
Please explain again with diagram.
Show more

Refer to if-each-curved-portion-of-the-boundary-of-the-figure-attached-is-forme-203894.html#p1562850
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If each curved portion of the boundary of the figure attached is forme 19 Oct 2018, 10:15
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Bunuel

If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)

Show Spoiler
Attachment:
Kaplan.png
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Hi chetan2u,

Two semi circles circumference makes one whole circle circumference. So basically in this question we have to find the surface area of a cylinder with a height of 4 cms and radius 2 cms

so \(2*\pi *2\) *4 = \(16\pi\)
what's wrong with this logic ? Why is this not leading to the answer?
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If each curved portion of the boundary of the figure attached is forme 20 Oct 2018, 06:55
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Bunuel

If each curved portion of the boundary of the figure above is formed from the circumference of two semicircles, each with a radius of 2, and each of the parallel sides has length 4, what is the area of the shaded figure?

A. 16
B. 32
C. \(16-8\pi\)
D. \(32-8\pi\)
E. \(32-4\pi\)

Show Spoiler
Attachment:
Kaplan.png

Hi chetan2u,

Two semi circles circumference makes one whole circle circumference. So basically in this question we have to find the surface area of a cylinder with a height of 4 cms and radius 2 cms

so \(2*\pi *2\) *4 = \(16\pi\)
what's wrong with this logic ? Why is this not leading to the answer?
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You are going wrong because you are taking it as a 3-d figure whereas it is just a 2-dimensional figure or a figure on a page..
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If each curved portion of the boundary of the figure attached is forme 27 Oct 2018, 07:03
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* Each of the parallel side as 4 cm- For which the given figure above will be a square.

Area of square = 16
Area of 2 circle with radius 2 = 8pi^2

Area of shaded portion - 16- 8pi

(All Area in sq.cm and radius in cm)

Please let me know my mistake in solving the problem
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If each curved portion of the boundary of the figure attached is forme 13 Nov 2021, 23:46
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