Math Is Fun Forum

loida

Member

Registered: 2009-11-12

Posts: 32

Volume of Rotation

I'd like to check if i got correct answer

Find the volume of the solid generated by rotating the region trapped between

around the y-axis.

i get

i was using formula

then

Last edited by loida (2010-12-28 13:53:21)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Hi loida;

What did you get when you drew the region you are interested in?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Volume of Rotation

hi loida

edit complete

I always start these with a diagram:

The line y = 1 forms the lower constraint;  x = 5 is the right hand constraint; and y = x forms the top constraint.

Note:  It is rotated around the y axis.

The dotted rectangle represents a 'typical' thin strip with width (5-y) and thickness dy.

So that 'rectangle', (5 - y) by dy, is rotated to make a disc (with hole) with volume pi (5 squared - y squared) times thickness

Now sum these up across the y direction:

Sorry, this does not give your answer.

Bob

Last edited by Bob (2010-12-28 22:17:17)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Hi;

That is the correct diagram but how about this idea. We square that triangle up now it is a 4 x 4 square. If we rotate that around the y axis it is just a washer. The volume of the washer is

The line y = x cuts that washer in half so the volume of that triangle rotated around the y axis is 48 π. Where is that going wrong?

I got your answer using calculus but you might have left out a pi in front.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Volume of Rotation

hi bobbym,

When you 'cut your washer in half' you make a cone.  So I don't think you can just take half the answer.

ps.  Firstly I rotated around the x axis;  then I messed up the volume calculation.  What I've edited above is my best answer so far.  It may not be the version you read earlier.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Yes, I know, a cone with r and h is 1 / 3 of a cylinder with the same r and h. So that cone is 32 π. That means the bottom volume which we are interested in is 64 π. That does not jive with the 176 / 3 π answer that calculus gives.

Oh, I see it now. 1 / 3 of cylinder but not 1 / 3 of a washer! The calculus answer stands!

Loida;

Just in case you did not always draw a diagram whenever you can.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

thanks .. i missed 1<=y part .. i drew y<=1

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Hi;

Check this vid out!

http://www.youtube.com/watch?v=Y4tHgy0XiUM

It is a good one. You did not have to subtract the interior cylinder the method just does the part you want.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

i  got 

the same u get in

Last edited by loida (2010-12-28 23:32:04)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Volume of Rotation

hi loida and bobbym,

I'm getting 136/3 times pi.  ??

loida:  Where did your equation come from?  Why 2 pi ?

Bob

Last edited by Bob (2010-12-28 23:55:46)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

i'm getting pi*176/3 in both cases 

http://en.wikipedia.org/wiki/Solid_of_revolution  Cylinder method

Last edited by loida (2010-12-29 00:24:59)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Hi;

I am getting 176 / 3 π.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

thank you!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

But remember up there you have 175 / 3 π. That is what started this whole thread.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

i know.. it's because i didn't see that it's y>=1
i'm thankful to both of you Bobies

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

i'm thankful to both of you Bobies

Now that is cool! I have never seen that thanks before and I thank you for posting it. Have a Happy New Year.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

loida

Member

Registered: 2009-11-12

Posts: 32

Re: Volume of Rotation

you too!
both of you

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Volume of Rotation

hi

Whoops!  I did 125 - 25 = 120.  And then 360 - 124 = 136.  !!  I blame it on all that wine over Christmas.

Thanks for sorting me out.

Happy New Year!

Bob

Last edited by Bob (2010-12-29 01:19:45)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Did you see Loida's thanks? Happy New Year!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Volume of Rotation

Yes.  I've never been called that either.  Perhaps it should be Bobbies.

Either way, I am honoured to be mentioned in the same sentence as you.  That's twice today.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Volume of Rotation

Hi Bob;

Either way, I am honoured to be mentioned in the same sentence as you.  That's twice today.

I think some clarification is necessary.

Ever seen any of those old Godzilla movies? Shown here on the left doing the Tango with King Kong. They would stuff some poor guy into that bad rubber suit until he would expire from heat exhaustion. They would literally pick him up with a forklift and place him in the middle of a cardboard city. He could hardly move in that rubber coffin, so he would frequently flop and require the forklift. Me working on a math problem is very much like watching Godzilla stumble through Tokyo, if I stumble enough I might find some answer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.