Aptitude - Volume and Surface Area - Discussion

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"Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."
- Albert Einstein

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

[A]. 12 cm3[B]. 15 cm3
[C]. 16 cm3[D]. 20 cm3

Answer: Option


Clearly, we have r = 3 cm and h = 4 cm.

Volume = 1 r2h = 1 x x 32 x 4 cm3 = 12 cm3.
3 3

Sachin.Nani3@Gmail.Com said: (Wed, Feb 15, 2012 07:56:22 PM)    
I could not understand, please explain any body.

Shafi said: (Fri, Mar 23, 2012 02:39:18 PM)    
Since triangle is rotated with a side of 3 hence radius=3, volume=1/3*22/7r^2h.

Vinay Vidhani said: (Sun, Jul 1, 2012 02:37:24 AM)    
We know that long side in right angle triangle is hypotenuses OK let 3 is base and 4 is a height then put the formula of volume of cone is 1/3 *pai r*r*h that's all.

Vinay Vidhani said: (Sun, Jul 1, 2012 02:39:31 AM)    
But how can we understand that 3 will base ?

Uday Kiran.M said: (Mon, Jul 9, 2012 01:37:07 PM)    
There is no need that the rotated side must be the base. You can rotate around the opposite side of triangle then also you will get the same cone.

Vidhya said: (Sat, Aug 11, 2012 08:16:57 PM)    
If the side of 3cm is rotated, won't it become the height of the cone ?

Ranjan said: (Tue, Aug 21, 2012 04:36:14 PM)    
I can't understand.

Deepika said: (Sat, Jan 12, 2013 06:03:28 PM)    
We know long side is hypotenuse according to question which will be 5cm then height is 4cm & base is 3cm then we extent the 3cm behind 4cm height as a diameter & draw the circle along this & calculate the volume from formula.

Josh said: (Sun, Mar 24, 2013 09:09:34 AM)    
We take orderly the sides of triangle in required it is simply to calculate using formula 1/3*3.14*r^2*h.

Sakshi said: (Wed, May 15, 2013 05:04:14 PM)    
If it is rotated about 3 cm. How could radius be 3 cm?

Anonymous said: (Tue, Jun 4, 2013 09:46:22 PM)    
Is the cone with base 3 rotated (form imaginary cone shape) or is it folding it (say paper) to form cone? if so how its r=3?

Silky said: (Thu, Sep 26, 2013 12:18:27 PM)    
@Sakshi is right. If it is rotated about 3 cm then its radius should be 3/2 = 1.5 cm.

Laraib said: (Mon, Nov 25, 2013 11:36:58 PM)    
Tell me basics of volume and surface area.

Yasir Arafat Jubel said: (Tue, Dec 10, 2013 05:07:54 PM)    
Which mean r & h?

Gini said: (Wed, Dec 25, 2013 08:17:09 PM)    
I think 3 cm is the surface area of the circle at the base.

Then, 3 cm=22/7*r*r.

Tony said: (Fri, Apr 25, 2014 07:05:58 PM)    
It can be done without knowing the formulae for the volume of a cone. Initially work out the volume of a cylinder with base 3cm and height 4 cm. The volume swept through rotation for the cylinder would be 113.04 cubic cm. Now visualize how many cones it would take to sweep the same volume as the cylinder (it is 3 - one above inverted and 1 side on 90 degrees). Divide 113.04 by 3 which gives the correct answer.

Pritam said: (Mon, May 5, 2014 05:50:02 PM)    
Why should the base be taken as 3? why can't it be 4? what's the logic?

Pintu said: (Mon, Jun 2, 2014 08:42:27 AM)    
It is not mentioned that it is rotated with 3 cm it can be rotated about 3 cm, then in that case 3cm will be the height and 4 cm will be the radius.

Asim said: (Mon, Jun 16, 2014 12:20:19 AM)    
If the question says the triangle is rotated keeping side of 3 cm fixed then the side of 3cm will be the height and 4 cm will be the radius.

Ankush said: (Wed, Jun 18, 2014 04:40:10 PM)    
If the cone is made by rotating the side which is 3 then 3 will become the circumference of the base being 2pie r. Hence 2pie r = 3 and r = 3/2pie.

Is it correct?

King said: (Fri, Jun 20, 2014 11:39:58 AM)    
The Triangle is rotated about the side 3 so it should be the height and the radius should be 4 and According to volume formula to cone its (1/3)*pi*r*r*h in should be 16*pi.

Rohit said: (Sat, Dec 13, 2014 10:52:40 PM)    
The only possible explanation is that it is rotated about, not revolved about.

If 5th rotates it means it runs around a fixed center. It rotates about 3 cm side means the 3 cm side is rotating.

Nameera Khan said: (Thu, Feb 5, 2015 10:20:03 PM)    
How can we know the height is 4 its not given even it can be 5 also did not understand please explain?

Khushi said: (Fri, May 29, 2015 03:40:07 PM)    
As it is mentioned that the triangle is rotated to the side 3 cm. That's the reason it has become the radius of the so formed cone. It has nothing to do with whether it (3 cm side) is considered the base or the height of the triangle!

Prabhu said: (Mon, Jun 8, 2015 11:20:07 AM)    
If it is rotated along the side with 3cm then how could radius be 3cm?

Swati said: (Sat, Jun 27, 2015 08:42:35 AM)    
Anyone solve this last step of questions?

My answer is not coming 12. I think wrong answer.

Kanwar Pal Singh said: (Tue, Jul 14, 2015 09:45:35 PM)    

I think you are solving with value of "pi". Otherwise the calculation shit is so simple.

Sravanthi said: (Wed, Aug 19, 2015 12:57:29 PM)    
It is not mentioned that 3 is base and 4 is height. Why can't 3 be height and 4 be base? please explain.

Vish said: (Wed, Aug 19, 2015 01:01:06 PM)    
Guys, they said triangle is rotated the 3 cm side to form a cone. So the only way the cone can b formed from a right angle triangle is by rotating base and its 3 cm in this case!

Pankaj Dhariwal said: (Thu, Aug 27, 2015 12:31:13 PM)    
I can't understand. In this question where we use 5cm. Please explain.

Rama said: (Sun, Sep 6, 2015 07:41:05 PM)    
Since triangle is rotated with side of 3 cm hence radius is 3.

Clearly, we have v-1/3*r*r*h.

V!Cky said: (Sat, Oct 3, 2015 09:50:55 PM)    
@Sakshi and other who doubt in radius @ read question carefully.

i.e rotated the side of 3 cm to form a cone.

Diameter = 2*Radius.

Tina said: (Mon, Nov 16, 2015 12:47:29 AM)    
If 3 cm side is rotated, shouldn't it form circumference of cone?

Then 2*pie*r = 3.

How can r itself be 3 here?

Suhail said: (Mon, Nov 23, 2015 12:35:44 PM)    
Dear friend,

As it is moved along the side 3 cm hence this 3 cm will be distributed entire circumference.

So 3 = 2*22/7*r.

r = 3/2Π.

Srikanth said: (Mon, Dec 21, 2015 09:08:43 PM)    
Volume of cone is (1/3)*pi*r*r*h = (1/3)*(22/7)*3*3*4 then, the value will be 12(22/7)cm^3.

Aashish said: (Wed, Jan 20, 2016 08:01:04 PM)    
We can take 4 as base. And according to which volume will be 16*pi or remove 16*pi from the options.

Or we can have only one correct option either 12pi or 16pi.

Shinu said: (Sat, Feb 20, 2016 03:42:38 PM)    
Pi factor should be included.

Archana said: (Fri, May 27, 2016 02:09:15 PM)    
How you take 3cm for the base?

Please, Explain.

Mia Khalifa said: (Fri, May 27, 2016 05:08:58 PM)    
Why the 3 cm is taken as the radius?

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