Aptitude - Volume and Surface Area - Discussion
Discussion Forum : Volume and Surface Area - General Questions (Q.No. 1)
1.
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:
12
cm3
cm315 cm3
cm316 cm3
cm320 cm3
cm3Answer: Option
Explanation:
Clearly, we have r = 3 cm and h = 4 cm.
 Volume = |
1 | r2h = |
 |
1 | x x 32 x 4 |
 cm3 |
= 12 cm3. |
| 3 | 3 |
Video Explanation: https://youtu.be/Njsid2mVwUY
Discussion:
77 comments Page 1 of 8.
Tony said:
1 decade ago
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.
Sateesh kumar Routhu said:
9 years ago
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.
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.
Abhinav said:
8 years ago
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.
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:
8 years ago
@ALL.
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.
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.
Madhavi said:
9 years ago
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.
Then,
3^2 + 5^2! = 4^2.
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.
Then,
3^2 + 5^2! = 4^2.
RAHUL robin said:
7 years ago
Incorrect/missing preposition in the question makes it confusing as one can't get whether the triangle is rotated with/about the side of 3 cm.
If it's rotated with the side of 3 cm then r=3, h=4. If it's rotated about the side of 3 cm then r=4, h=3.
If it's rotated with the side of 3 cm then r=3, h=4. If it's rotated about the side of 3 cm then r=4, h=3.
(2)
Stragi said:
3 years ago
As the base is 3.
How can the radius will be 3?
Why can't it (3) be a perimeter which is equal to 2*3.14*r.?
And also if it is rotated as base 3 then 4, 5 lengths will be slant heights and (4, 5 are not equal and can't make a perfect cone also).
How can the radius will be 3?
Why can't it (3) be a perimeter which is equal to 2*3.14*r.?
And also if it is rotated as base 3 then 4, 5 lengths will be slant heights and (4, 5 are not equal and can't make a perfect cone also).
(5)
Deepika said:
1 decade ago
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.
Khushi said:
1 decade ago
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!
DEV RAJ said:
8 years ago
Right triangle is rotated on the axis at 90*, the side of 3 cm is rotated along the axis so diameter is 6 and are = 3.
It is given, if we are rotating on the side 3cm it must be base "see the diagram".
It is given, if we are rotating on the side 3cm it must be base "see the diagram".
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers