Finding the Volume of Cones and Cylinders Using Known Values

[Kirito123]

Homework Statement

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.

 

[Kirito123]

That is the exact wording there is nothing else to it, i might have not understood or it just doesn't make sense..

 

[Dank2]

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 ?

 

[Dank2]

you can't do it without knowing at least the radius or the height.

the height and radius is the same of both objects

 

[Kirito123]

yea they both have the same height and radius but i still can't find out the height or radius with just the volume.

 

[Dank2]

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.

 

[Kirito123]

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 going to 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

 

[Dank2]

360/ 3.14 = 114.64

Why did you do that?

 

[Kirito123]

don't you multiply 3.14 by 360, the reverse of that would be division.

 

[Dank2]

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.

 

[Kirito123]

Sorry just so I am clear what are you referring to when you say "first equations". Do you mean the volume of the cone or

120 x 3

 

[Dank2]

Sorry just so I am clear what are you referring 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

 

[Dank2]

Sorry just so I am clear what are you referring 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

 

[Kirito123]

Ok just making sure so i don't mess up. If i multiply it by 3 it would become 3 Pi(h)r²??

 

[Dank2]

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?

 

[Kirito123]

wait doesn't the multiplied 3 cancel out the other division one?

 

[Dank2]

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

 

[Kirito123]

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.

 

[Dank2]

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)

 

[Kirito123]

it would = 1

 

[Dank2]

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 = ?

 

[Kirito123]

sorry for late reply, anyway 3 * the volume of the cone would be 360.

 

[Kirito123]

since 3 x 120 = 360 as i said before right?

 

[Dank2]

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

 

[Kirito123]

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?

 

[Dank2]

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?

 

[Dank2]

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?

 

[Kirito123]

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.

 

[Dank2]

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.

 

[Kirito123]

Pi(h)r² ??

 

[Kirito123]

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 I am 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.

 

[olgerm]

Write all equations and information to one equation system and think, if you can mathematically solve this for V_silinder.