What is the Volume of a Solid of Revolution Rotated about the x-axis?

[Joe_K]

Homework Statement

Find the volume obtained by rotating the solid about the specified line.

y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.

Homework Equations

I used the disk method

The Attempt at a Solution

I drew a sketch and used disk method. For the radius I used 2-(1/2)x with a height of 1, and integrated. For an answer, I came up with 5pi/4. Does this seem correct? Thanks!

 

[tylerc1991]

For an answer, I came up with 5pi/4. Does this seem correct? Thanks!

I am getting a different answer. What are your bounds? What is the integrand?

 

[Joe_K]

I am getting a different answer. What are your bounds? What is the integrand?

My bounds were from 1 to 2.

 

[tylerc1991]

My bounds were from 1 to 2.

That is correct. What about the integrand?

 

[SammyS]

Homework Statement

Find the volume obtained by rotating the solid about the specified line.

y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.

Homework Equations

I used the disk method

The Attempt at a Solution

I drew a sketch and used disk method. For the radius I used 2-(1/2)x with a height of 1, and integrated. For an answer, I came up with 5pi/4. Does this seem correct? Thanks!

What do you mean by "with a height of 1" ?

What function did you integrate?

 

[Joe_K]

What do you mean by "with a height of 1" ?

What function did you integrate?

Sorry, I don't know why I typed height, I meant to say that that the bounds were 1 to 2. For the integrand I just had pi*2-(1/2)x*1 dx

 

[tylerc1991]

For the integrand I just had pi*2-(1/2)x*1 dx

The area of one of the disks is going to be \pi \cdot (2 - \frac{1}{2} x)^2. What happens when we sum those disks from x = 1 to x = 2?

 

[Joe_K]

The area of one of the disks is going to be \pi \cdot (2 - \frac{1}{2} x)^2. What happens when we sum those disks from x = 1 to x = 2?

I think I forgot to square the radius when I originally did it. I redid the problem and came up with 19pi/12. Is this still wrong?

 

[tylerc1991]

I think I forgot to square the radius when I originally did it. I redid the problem and came up with 19pi/12. Is this still wrong?

That is the answer I got.

 

[Joe_K]

Awesome. Thanks guys!