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The figure above is constructed by separating a circular region into 6
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Bunuel
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The figure above is constructed by separating a circular region into 6 [#permalink] New post  26 Apr 2019, 05:38
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The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)


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BrentGMATPrepNow
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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  26 Apr 2019, 09:42
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Bunuel wrote:
Image
The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)
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Attachment:
2019-04-26_1735.png


Let's examine one sector.
Image
If the diameter = d, then the radius = d/2
Also notice that each curved arc is 1/6 the circumference of the original circle

So, each part of the perimeter is as follows:
Image

Perimeter = d/2 + d/2 + (1/6 of circumference) + (1/6 of circumference) + (1/6 of circumference) + (1/6 of circumference) + (1/6 of circumference) + (1/6 of circumference)
= d + circumference of circle

circumference of circle = (π)(diameter)
So, circumference of original circle = πd

So, perimeter = d + πd

Answer: D

Cheers,
Brent
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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  26 Apr 2019, 07:55
IMO D

circle is divided into 6 equal parts

so angle at center = 60

so length of arc = 2*pie*(d/2)*(60/360)

= pie*d/6

so the total perimeter = 6*pie*d/6 + d

d is the sum.of two staright side

award kudo if helpful

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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  28 Apr 2019, 03:28
dia= d
rad=d/2
and circumference = 2*pi * d/2 ; pi * d
each side of circumference is pi*d/6
so total sum ; 6*pi*d/6 + d/2+d/2
IMO D \(\pi d + d\)


Bunuel wrote:
Image
The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)


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stne
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The figure above is constructed by separating a circular region into 6 [#permalink] New post  07 May 2019, 10:51
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Bunuel wrote:
Image
The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)


PS44602.01
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Attachment:
2019-04-26_1735.png


The length of the figure consists of 3 arcs at top and 3 arcs at bottom , these form the whole circumference of the circle.
\(2*\pi *\frac{d}{2} = \pi*d\) hence the length = \(\pi*d\)

The two straight edges are the radius, and form the diameter when added together \(r+r =d\)
hence perimeter =\(\pi*d+d\)
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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  23 May 2019, 04:16
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Solution


Given
In this question, we are given
    • A diagram, which is constructed by separating a circular region into 6 equal parts and rearranging them, as shown in the diagram.
    • The diameter of the circle is d.

To Find
We need to determine
    • The perimeter of the figure, as shown.

Approach & Working
The perimeter of the given figure consists of 2 parts:
    • 6 equal length arcs, which together form the perimeter of the circle
    • 2 equal line segments, each of which is equal to the radius of the circle

The total length of the 6 arcs = the perimeter of the circle = 2π * d/2 = πd
The total length of the 2 line segments = d/2 + d/2 = d
    • Therefore, the perimeter of the given figure = πd + d

Hence, the correct answer is option D.

Image

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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  23 May 2019, 16:11
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Bunuel wrote:
Image
The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)


PS44602.01
Quantitative Review 2020 NEW QUESTION

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Attachment:
2019-04-26_1735.png


The perimeter of the figure is the circumference of the circle plus twice the radius (i.e., the diameter). Therefore, the perimeter is πd + d.

Answer: D
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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  19 Nov 2020, 04:04
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Bunuel wrote:
Image
The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

A. \(\pi d\)
B. \(2\pi d\)
C. \(\pi d + 2\)
D. \(\pi d + d\)
E. \(2\pi d + d\)


PS44602.01
Quantitative Review 2020 NEW QUESTION

Show Spoiler
Attachment:
2019-04-26_1735.png



As the figure is constituted dividing a whole a circle, So the perimeter will include the perimeter of the whole circle \(\pi d\) and two outer sides (radii) of the figure.

Thus the perimeter will be \(\pi d + d\)

The Answer is D
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Re: The figure above is constructed by separating a circular region into 6 [#permalink] New post  08 Dec 2020, 21:09
OFFICIAL GMAT EXPLANATION

The perimeter consists of 6 arcs and 2 segments. The total length of the 6 arcs is the circumference of the circle, which is πd. Each segment is a radius of the circle with length d/2. Therefore the perimeter of the figure is πd + 2*(d/2) = πd + d.
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Re: The figure above is constructed by separating a circular region into 6 [#permalink]
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