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

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

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New post 18 Mar 2012, 11:05
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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.

Can you please help?
[Reveal] Spoiler: OA

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MGMAT 1 --> 530
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GMAT ==> 730

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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
Pizza.jpeg [ 114.3 KiB | Viewed 5939 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.

Answer: D.

Hope it's clear.
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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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New post 19 Mar 2012, 03:05
Bunuel - Lovely example thanks. But how come the area will be 2 pi?
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GMAT ==> 730

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

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

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New post 19 Mar 2012, 04:06
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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 :-P
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Re: A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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New post 28 Mar 2016, 02:44
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A circular pizza is cut into eight wedge-shaped slices of [#permalink]

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New post 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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New post 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.

Can you please help?



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

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