Volumes and heights of cones.

  • Thread starter Kirito123
  • Start date
  • #1
Kirito123
125
14

Homework Statement



upload_2016-5-12_18-58-44.png

Homework Equations


volume of cone = pi(r)2h / 3
volume of cylinder = pi(r)2h

The Attempt at a Solution


How can I do this, all they give is the volume and we know the value of pi ( 3.14159). I tried but you can't do it without knowing at least the radius or the height.
 

Answers and Replies

  • #2
Kirito123
125
14
That is the exact wording there is nothing else to it, i might have not understood or it just doesn't make sense..
 
  • #3
Dank2
213
4
That is the exact wording there is nothing else to it, i might have not understood or it just doesn't make sense..
By just looking at the equation you have written, What do you need to do the cylinder volume in order to get the cone volume ?
 
  • #4
Dank2
213
4
you can't do it without knowing at least the radius or the height.
the height and radius is the same of both objects
 
  • #5
Kirito123
125
14
yea they both have the same height and radius but i still can't find out the height or radius with just the volume.
 
  • #6
Dank2
213
4
yea they both have the same height and radius but i still can't find out the height or radius with just the volume.
look again at the equations you have written, and only at them. what is the same and what is different, type it here.
 
  • #7
Kirito123
125
14
volume of cone = pi(r)2h / 3
volume of cylinder = pi(r)2h

They both use pi and the radius is squared, only different is for a cone you have to divide by 3. I'm gonna take a crack at it but it might be wrong.
So to find the radius we would do as shown below :

120 x 3 (we are reversing the original formula)

360/ 3.14 = 114.64

114.64 squared are equal to 10.707.

So the radius of both
 
  • #9
Kirito123
125
14
don't you multiply 3.14 by 360, the reverse of that would be division.
 
  • #10
Dank2
213
4
don't you multiply 3.14 by 360, the reverse of that would be division.
no need to. we need to find the volume of the cylinder.

What happens if you multiply by 3 your first equation. don't use the 120 yet. just the first equation.
 
  • #11
Kirito123
125
14
Sorry just so im clear what are you refering to when you say "first equations". Do you mean the volume of the cone or
120 x 3
 
  • #12
Dank2
213
4
Sorry just so im clear what are you refering to when you say "first equations". Do you mean the volume of the cone or
this is the first equation you have written pi(r2)2h / 3 = Volume of cone
 
  • #13
Dank2
213
4
Sorry just so im clear what are you refering to when you say "first equations". Do you mean the volume of the cone or
no numbers yet, just use the parameters, manually multiply it by 3 and type what you got
 
  • #14
Kirito123
125
14
Ok just making sure so i don't mess up. If i multiply it by 3 it would become 3 Pi(h)r2??
 
  • #15
Dank2
213
4
Ok just making sure so i don't mess up. If i multiply it by 3 it would become 3 Pi(h)r2??
wasn't there a /3 aswell? where did it go?
 
  • #16
Kirito123
125
14
wait doesn't the multiplied 3 cancel out the other division one?
 
  • #17
Dank2
213
4
wait doesn't the multiplied 3 cancel out the other division one?
Type it all down from the start, don't show only the result , and let's see
 
  • #18
Kirito123
125
14
wait doesn't the multiplied 3 cancel out the other division one?

wait that only works if it was a division 3 that cancels a division 3.
 
  • #19
Dank2
213
4
wait that only works if it was a division 3 that cancels a division 3.

1/3 * 3 = ? any division by three can be written as x/3 = x* (1/3)
 
  • #20
Kirito123
125
14
it would = 1
 
  • #21
Dank2
213
4
it would = 1
So looks like it would cancel one another. don't forget we need to multiply both sides of the equation always when we want to multiply one side we must multiply the other aswell, so equation will hold.

3* pi(r2)h / 3 = 3* Volume of cone = ?
 
Last edited:
  • #22
Kirito123
125
14
sorry for late reply, anyway 3 * the volume of the cone would be 360.
 
  • #23
Kirito123
125
14
since 3 x 120 = 360 as i said before right?
 
  • #24
Dank2
213
4
since 3 x 120 = 360 as i said before right?
You jump too fast to the numbers .

3* pi(r2)h / 3 = pi(r2)h = 3* Volume of cone
we multiplied by 3 so it cancels with /3, and the volume got multiplied by 3.

but what is pi(r2)h ? remember that r and h are the same
 
  • #25
Kirito123
125
14
pi(r2)2h

Why did you put r2 and then 2h? and now i get what your saying, i have to find a radius and height that would be equal to 3 * volume of the cone?
 
  • #26
Dank2
213
4
Why did you put r2 and then 2h? and now i get what your saying, i have to find a radius and height that would be equal to 3 * volume of the cone?

that was a mistake, fixed it.

3* pi(r2)h / 3 = pi(r2)h = 3* Volume of cone

take a look at your second equation that you have written at the first message. pi(r2)h is equal to what?
 
  • #27
Dank2
213
4
Why did you put r2 and then 2h? and now i get what your saying, i have to find a radius and height that would be equal to 3 * volume of the cone?
Volume of the cylinder is equal to what?
 
  • #28
Kirito123
125
14
its equal to 360 right. I'm saying this since if you where to multiply 3 x 120 you would get 360 and that 360 would represent pi(r2) h.
 
  • #29
Dank2
213
4
Why did you put r2 and then 2h? and now i get what your saying, i have to find a radius and height that would be equal to 3 * volume of the cone?
it's written in the second equation, just need to copy paste really.

then plug it
its equal to 360 right. I'm saying this since if you where to multiply 3 x 120 you would get 360 and that 360 would represent pi(r2) h.
Summary:

Multiply first equation by 3 you get : 3* pi(r2)h / 3 = 3* Volume of cone. simplfy left side you get pi(r2)h = 3*Volume of cone.

but hey pi(r2)h is equal to volume of the cylinder from equation 2, so we plug it above, and get volume of the cylinder = 3*Volume of cone.

Now you do know the volume of the cone. and so we got the answer just by multiplying by 3.

Note that all of this holds because radius and height was the same.
 
  • #30
Kirito123
125
14
upload_2016-5-12_20-48-23.png

Pi(h)r2 ??
 
  • #31
Kirito123
125
14
I was just reading over a lesson and i found this "Similar to the relationship between the prism and the pyramid, the volume of three cones fits into a cylinder with the same radius and height.", If im correct that's stating that 360 is the volume of the cylinder and 120 is the volume of the cone. I think that might be right ;3

In short 360 = volume of cylinder and 120 = volume of cones.
 
  • #32
olgerm
Gold Member
507
32
Write all equations and information to one equation system and think, if you can mathematically solve this for Vsilinder.
 

Suggested for: Volumes and heights of cones.

Replies
2
Views
785
Replies
2
Views
12K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
9
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
12
Views
2K
Replies
5
Views
3K
Top