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 5 of 8.
Anil sarode said:
9 years ago
You are absolutely right @Rohit.
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.
Shivang said:
9 years ago
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:
9 years ago
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:
9 years ago
If we rotate 3cm side won't 3cm be the circumference of its base.
Aakriti said:
9 years ago
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.
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:
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.
Sameer said:
8 years ago
I could not understand yer, please help me by explaining it.
Lia US said:
8 years ago
Can anyone please explain me this? I didn't understand.
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.
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