Aptitude - Volume and Surface Area - Discussion


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 A


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: (Feb 15, 2012)  
I could not understand, please explain any body.

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

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

Uday Kiran.M said: (Jul 9, 2012)  
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: (Aug 11, 2012)  
If the side of 3cm is rotated, won't it become the height of the cone ?

Ranjan said: (Aug 21, 2012)  
I can't understand.

Deepika said: (Jan 12, 2013)  
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: (Mar 24, 2013)  
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: (May 15, 2013)  
If it is rotated about 3 cm. How could radius be 3 cm?

Anonymous said: (Jun 4, 2013)  
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: (Sep 26, 2013)  
@Sakshi is right. If it is rotated about 3 cm then its radius should be 3/2 = 1.5 cm.

Laraib said: (Nov 25, 2013)  
Tell me basics of volume and surface area.

Yasir Arafat Jubel said: (Dec 10, 2013)  
Which mean r & h?

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

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

Tony said: (Apr 25, 2014)  
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: (May 5, 2014)  
Why should the base be taken as 3? why can't it be 4? what's the logic?

Pintu said: (Jun 2, 2014)  
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: (Jun 16, 2014)  
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: (Jun 18, 2014)  
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: (Jun 20, 2014)  
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: (Dec 13, 2014)  
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: (Feb 5, 2015)  
How can we know the height is 4 its not given even it can be 5 also did not understand please explain?

Khushi said: (May 29, 2015)  
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: (Jun 8, 2015)  
If it is rotated along the side with 3cm then how could radius be 3cm?

Swati said: (Jun 27, 2015)  
Anyone solve this last step of questions?

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

Kanwar Pal Singh said: (Jul 14, 2015)  

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

Sravanthi said: (Aug 19, 2015)  
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: (Aug 19, 2015)  
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: (Aug 27, 2015)  
I can't understand. In this question where we use 5cm. Please explain.

Rama said: (Sep 6, 2015)  
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: (Oct 3, 2015)  
@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: (Nov 16, 2015)  
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: (Nov 23, 2015)  
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: (Dec 21, 2015)  
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: (Jan 20, 2016)  
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: (Feb 20, 2016)  
Pi factor should be included.

Archana said: (May 27, 2016)  
How you take 3cm for the base?

Please, Explain.

Mia Khalifa said: (May 27, 2016)  
Why the 3 cm is taken as the radius?

Lawrence said: (Jul 11, 2016)  
How can 3 be the radius since it's rotated?

Anil Sarode said: (Aug 27, 2016)  
You are absolutely right @Rohit.

Sateesh Kumar Routhu said: (Sep 3, 2016)  
Hello friends,

3, 4, 5 are the sides and hypotenus of the right angle triangle, i.e. root of 3^2 + 4^2 = 5, in this we can take either 3, 4 or 4, 3 as sides and 5 as a hypotenus. Then we take radious and height of the cone are r = 3, h = 4, or r = 4, h = 3.

We are able to form two cones of different sizes with same area and volume. i.e volume is 12 pi cm^3.

Shivang said: (Sep 19, 2016)  
The question is incomplete, it is not mentioned that the 3 cm is the base. And if it is then cone thus formed has symmetry about x-axis with height 3cm.

Vikash said: (Sep 26, 2016)  
According to me, the language of the question is wrong. Because if it is rotated by side 3cm, its radius will never be 3cm, if anybody visualizes it?

Kirti said: (Nov 12, 2016)  
If we rotate 3cm side won't 3cm be the circumference of its base.

Aakriti said: (Dec 10, 2016)  
1. A triangle with these dimensions doesn't form a cone.

2. Even if it does then the length of the side rotated would be the circumference of the base of the figure and not the radius.

Madhavi said: (Dec 17, 2016)  
We take 4 height because by using Pythagarous theorem the right angled triangle must want to satisfy the side1^2 + side2^2 =hupotenuous^2.
3^2 + 4^2 = 5^2.
25 = 25.

That's why here we take 4cm has a height.
Suppose if we take height has 5cm.
3^2 + 5^2! = 4^2.

Sameer said: (Feb 5, 2017)  
I could not understand yer, please help me by explaining it.

Lia Us said: (Apr 1, 2017)  
Can anyone please explain me this? I didn't understand.

Abhinav said: (Apr 5, 2017)  
See in the question it is mentioned that we are rotating the side of 3cm to form cone that means the axis about which we are going to rotate is perpendicular to the side of 3cm. Hence your radius will be 3cm.

Now, just use the formula for volume of cone = 1/3 * π * r^2 * h= 1/3 *π * 9 * 4 = 12πcm^3.

Sangeethaa Theivendran said: (Apr 22, 2017)  

Just imagine how you draw a circle with radius 3cm using compass. Now look at the shape between two legs of compass. It is a right triangle. Now, if the right triangle is rotated a cone is formed. So radius of cone's base= base of triangle and height of both cone and triangle are same.

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