Calculus Lovers, I'm calling you out!!

[trilobyte]

How do I get the volume of the slab/wedge below? I'm having a problem as to where to start in finding the integral

http://www.voidyourwarranty.net/images/trilobyte/untitled.JPG

*pretend those are uniformed curves

Thanks!

 

[Evadman]

if you feel like posting some numbers, I could do it in my head and explain it to ya, but I suck at forumlas. That is why I hated when I had to "show all work"

<edit>
And yes, I am serious

 

[Mr.IncrediblyBored]

Originally posted by: trilobyte
Calculus Lovers, I'm calling you out!!

Yep, both of you!

By the way, you can't do direct image links here.


www.voidyourwarranty.net/images/trilobyte/untitled.JPG

 

[trilobyte]

I just need someone to explain it a little, i think i can figure it out from there

And no, there are no numbers, that's all the info given...

 

[Evadman]

That and are from a link maker for a YaBB board.

Ill make my own numbers. Gimme a minute.

 

[GoodToGo]

Umm I dont get the picture. Is the cylinder "torn" or what?

 

[Mr.IncrediblyBored]

Originally posted by: GoodToGo
Umm I dont get the picture. Is the cylinder "torn" or what?

Imagine a plane intersecting all the way through the bottom right portion of the cylinder. He needs to find the volume of the small "wedge" cut out of the cylinder.

 

[Evadman]

Ok , lets make it easy then.

To make it easier I will number everything. New sections numbered

The angle is 45 degrees.
The radius is 2

usee your nifty graphing calculator to find the length of A. B is the bottom of that triangle, which is also the radius r. Since that angle is a nice 45 degrees, then we know without a calculator, that A is exactly 1/2 of the radius, or bottom of the triangle. or 1.

D is the diameter, or 2r. So we get 4.

So we have:

A= 1
B= 2

Using pathagreans therom, 1^2 + 2^2 = C^2 or C = square root 5. (2.2306)

A= 1
B= 2
C= 2.2306
D= 4

Now we figure out the section of cylander that A goes up to. You have the height, 1. And you have the radius, 2. Then you can figure out the volume in that cylinder. this part

Then, ( and this is the part I just made up, but It should work) take the degree from that angle, and take it as a percentage of 180. Or in this instance, 45 / 180 = .25 or 25% then, multiply the voluem you got earlier by .25 and you should get your answer.

 

[trilobyte]

???

i appreciate the help, but that makes to sence in terms of setting up the integral

 

[Evadman]

Originally posted by: trilobyte
???

i appreciate the help, but that makes to sence in terms of setting up the integral

Who was setting anything up? I showed you how to solve the problem This is how I went though college. I never did anything how you were supposed to, but yet, I solve problems easily, and usually got the right answer

Someone check my math with however you are supposed to do this, and tell me if I am correct, or wrong. I promise not to yell if I am wrong

<edit>
I will make it extreamly easy. I will make an equation you can just put those #'s into, and get the answer. Gimme a minute.

Using the diagram I have above,
(pi r^2 * A) * ("Degree listed for theta" / 180) = the volume of that slice

 

[rgwalt]

Originally posted by: Evadman
Ok , lets make it easy then.

To make it easier I will number everything. New sections numbered

The angle is 45 degrees.
The radius is 2

usee your nifty graphing calculator to find the length of A. B is the bottom of that triangle, which is also the radius r. Since that angle is a nice 45 degrees, then we know without a calculator, that A is exactly 1/2 of the radius, or bottom of the triangle. or 1.

D is the diameter, or 2r. So we get 4.

So we have:

A= 1
B= 2

Using pathagreans therom, 1^2 + 2^2 = C^2 or C = square root 5. (2.2306)

A= 1
B= 2
C= 2.2306
D= 4

Now we figure out the section of cylander that A goes up to. You have the height, 1. And you have the radius, 2. Then you can figure out the volume in that cylinder. this part

Then, ( and this is the part I just made up, but It should work) take the degree from that angle, and take it as a percentage of 180. Or in this instance, 45 / 180 = .25 or 25% then, multiply the voluem you got earlier by .25 and you should get your answer.

This seems right up to the last part. I don't think you need to look at (theta)/180 to find the volume percentage... I think it will always be 1/4 the volume of the smaller cylinder.

I don't really know how you would set this up as a calculus problem though.

Ryan

 

[Evadman]

rgwalt:

Your right. It will always be 1/4 of the smaller cyl. Its been to long
then the formula can just be:

pi r^2 * A) * .25

<edit>
Did I mention I love percentages? I love 'em. I drove my high school physics and electronics teachers crazy with them.

<edit #2>

Stop messing with my head rgwalt

 

[rgwalt]

Originally posted by: Evadman
rgwalt:

Your right. It will always be 1/4 of the smaller cyl. Its been to long
then the formula can just be:

pi r^2 * A) * .25

I'm not so sure that it is 1/4 after giving it more thought though... it would work just fine if it was a rectangular prism, but since it is a cylinder, I don't think it is right.

trilobyte: Do you have any idea of the equations of the curves?

Ryan

 

[Evadman]

Originally posted by: rgwalt

Originally posted by: Evadman
rgwalt:

Your right. It will always be 1/4 of the smaller cyl. Its been to long
then the formula can just be:

pi r^2 * A) * .25

I'm not so sure that it is 1/4 after giving it more thought though... it would work just fine if it was a rectangular prism, but since it is a cylinder, I don't think it is right.

trilobyte: Do you have any idea of the equations of the curves?

Ryan

Then my original formula would still work correct?
I see what you mean. If you "sweep out" that curve though 180 degrees, the curve will miss the "corners" or edges.

Your messing me up man

<edit>
Yep. If you substitue 35 degrees, you end up with a different percentage from 25%.

Is there any instance where (pi r^2 * A) * ("Degree listed for theta" / 180) = the volume of that slice doesn't work?