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# A right circular cone of radius 9 centimeter and height 12 cm is cut p

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Intern
Joined: 12 Sep 2017
Posts: 1
A right circular cone of radius 9 centimeter and height 12 cm is cut p [#permalink]

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Updated on: 12 Mar 2018, 23:52
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Question Stats:

67% (00:05) correct 33% (00:04) wrong based on 3 sessions

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A right circular cone of radius 9 cm and height 12 cm is cut parallel to the base , to form two pieces such that the height of smaller cone is half of the height of the frustum. What is the curved surface area, in square cm , of the frustum ?

1) 60π
2) 72π
3) 90π
4) 104π
5) 120π

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[Reveal] Spoiler: OA

Originally posted by Ritace on 12 Mar 2018, 22:34.
Last edited by Bunuel on 12 Mar 2018, 23:52, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 44599
A right circular cone of radius 9 centimeter and height 12 cm is cut p [#permalink]

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12 Mar 2018, 23:51
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Ritace wrote:
A right circular cone of radius 9 cm and height 12 cm is cut parallel to the base , to form two pieces such that the height of smaller cone is half of the height of the frustum. What is the curved surface area, in square cm , of the frustum ?

1) 60π
2) 72π
3) 90π
4) 104π
5) 120π

Sent from my A0001 using GMAT Club Forum mobile app

Not a GMAT question. One does not need to know the curved surface area of a frustum of a cone. Still:

We need to find he curved surface area of the lower part of the cone, so the area of the surface without the bottom and top. It's area = $$\pi*h*(R + r)$$.

Since the height is cut in the ratio 1:2, then the height of the frustum is $$h_1= 8$$ cm and the height of the smaller, upper cone is $$h_2= 4$$ cm. Next, from similar triangles property: $$\frac{r}{R} =\frac{h_2}{H}$$ (where H is the height of the big cone and h2 is the height of the smaller, upper cone). r/9 = 4/12 --> r = 3.

Therefore, the area of the frustum is $$\pi*h_1*(R + r)=\pi*8(9 + 3)=96\pi$$.

P.S. Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.

[Reveal] Spoiler:
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Intern
Joined: 26 Sep 2016
Posts: 7
Re: A right circular cone of radius 9 centimeter and height 12 cm is cut p [#permalink]

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13 Mar 2018, 00:19
It is said, that "height of smaller cone is half of the height of the frustum". Does not it mean, that h1 is 8 and h2 is 4???

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 44599
Re: A right circular cone of radius 9 centimeter and height 12 cm is cut p [#permalink]

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13 Mar 2018, 01:01
Jahfors wrote:
It is said, that "height of smaller cone is half of the height of the frustum". Does not it mean, that h1 is 8 and h2 is 4???

Thanks

Yes. Edited the typo.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: A right circular cone of radius 9 centimeter and height 12 cm is cut p   [#permalink] 13 Mar 2018, 01:01
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