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

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

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New post Updated on: 12 Mar 2018, 23:52
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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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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.
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A right circular cone of radius 9 centimeter and height 12 cm is cut p  [#permalink]

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New post 12 Mar 2018, 23:51
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:

Image

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.


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

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New post 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???

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

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New post 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 the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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