Volume: Washer Method

[JDM013]

Using the washer method, I need to find the volume of the shape bounded by y = sqrt(x+2), x = -2, y = 2...rotated about x = -3.

I get a Volume = 36.86. (outer radius = y^2 +1, inner radius = 1)

However my friend gets Volume = 3.35 (outer radius = y^2 -1, inner radius = -1)

Who is correct?

 

[Steven G]

Please show us your work and we will point out your error(s) if any.

 

[Dr.Peterson]

Using the washer method, I need to find the volume of the shape bounded by y = sqrt(x+2), x = -2, y = 2...rotated about x = -3.

I get a Volume = 36.86. (outer radius = y^2 +1, inner radius = 1)

However my friend gets Volume = 3.35 (outer radius = y^2 -1, inner radius = -1)

Who is correct?

How can a radius be -1? Try to draw such a circle!

But, how do they get a different volume that way? They're squaring the radius, aren't they? [EDIT: I missed the y^2 - 1]

@Jomo: some work was shown! But we do need to see the friend's work, to see how they got that answer.

 

[JDM013]

How can a radius be -1? Try to draw such a circle!

But, how do they get a different volume that way? They're squaring the radius, aren't they? [EDIT: I missed the y^2 - 1]

@Jomo: some work was shown! But we do need to see the friend's work, to see how they got that answer.

Thank you for your response - Turns out V = 36 was correct. It was fun exploring the different ways we could approx the volume from simple geometry -> multi variable calc.... Good problem!

 

[skeeter]

Cylindrical shells yields [MATH] V \approx 36.86[/MATH]
[MATH]V = 2\pi \int_{-2}^2 [x-(-3)] \cdot [2-\sqrt{x+2}] \, dx[/MATH]