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# A circular pizza is cut into eight wedge-shaped slices of

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Director
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A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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18 Mar 2012, 11:05
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Difficulty:

5% (low)

Question Stats:

93% (00:34) correct 7% (00:46) wrong based on 227 sessions

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A circular pizza is cut into eight wedge-shaped slices of equal size. What is the circumference of the pizza?

(1) The area of each slice measures 2pi square inches.

(2) The pizza measures 8 inches in diameter.

How come the answer is D?

This is how I doing it

Circumference of the pizza = 2*pi*r

Statement 1

Area of the arc = 2 pi

But we don't have an angle, therefore isn't this statement should be insufficient?

I understand statement B.

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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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18 Mar 2012, 13:27
3
A circular pizza is cut into eight wedge-shaped slices of equal size. What is the circumference of the pizza?

Here is an example of a circular pizza cut into eight wedge-shaped slices of equal size:
Attachment:

Pizza.jpeg [ 114.3 KiB | Viewed 8657 times ]
So, as you can see a circular pizza is cut into 8 equal segments.

(1) The area of each slice measures 2pi square inches --> the area of each segments is $$2\pi$$ --> the area of the whole pizza $$8*2\pi=16\pi$$ --> $$\pi*r^2=16\pi$$ --> $$r=4$$ --> the circumference is $$2\pi{r}=8\pi$$. Sufficient.

(2) The pizza measures 8 inches in diameter --> $$r=4$$ --> the circumference is $$2\pi{r}=8\pi$$. Sufficient.

Hope it's clear.
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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
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GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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19 Mar 2012, 03:05
Bunuel - Lovely example thanks. But how come the area will be 2 pi?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 46167
Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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19 Mar 2012, 03:08
enigma123 wrote:
Bunuel - Lovely example thanks. But how come the area will be 2 pi?

(1) says "the AREA of each slice measures $$2\pi$$ square inches"
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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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19 Mar 2012, 04:06
1
Hi,

Since the slices are equal size the angles will also be equal, thus statement 1 is sufficient

Bunuel, Thanks for the lovely explanation & the salivating picture
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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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27 May 2013, 05:30
Bumping for review and further discussion.
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A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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29 Jul 2016, 03:56
Bunuel wrote:
Bumping for review and further discussion.

Since it is divided into 8 equal parts ,entire angle is also divided into 8 parts ie 360/8 is angle subtended by one piece of pizza
therefore area of 1 piece= pi*r^2*Θ/360
(1) pi*r^2*Θ/360=2*pi
As Θ=360/8 substituting we get
r=4
thus circumference=8pi
suff..
(2) r=4
thus circumference=8pi
suff..

Ans D
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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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05 Sep 2017, 16:36
enigma123 wrote:
A circular pizza is cut into eight wedge-shaped slices of equal size. What is the circumference of the pizza?

(1) The area of each slice measures 2pi square inches.

(2) The pizza measures 8 inches in diameter.

How come the answer is D?

This is how I doing it

Circumference of the pizza = 2*pi*r

Statement 1

Area of the arc = 2 pi

But we don't have an angle, therefore isn't this statement should be insufficient?

I understand statement B.

Statement 1

If the slices are of equal size the the sum of all pieces allow to find the radius of the circle- in any case the sum of the pizza slices would be the total area of the circle.

16pi =pi r^2

Statement 2

Clearly because we can find the radius

D
Re: A circular pizza is cut into eight wedge-shaped slices of   [#permalink] 05 Sep 2017, 16:36
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