Calculating Volume of Revolution: Bounded Figure Rotated about y = -1

Thread starter ChaoticLlama
Start date Dec 12, 2006
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Revolution Volumes

In summary, to calculate the volume of revolution for a bounded figure rotated about y = -1, you can use the formula V = π∫(R(x)^2 - r(x)^2) dx, where R(x) is the outer radius and r(x) is the inner radius. The outer radius is the distance from the axis of revolution to the outer edge of the figure, while the inner radius is the distance from the axis of revolution to the inner edge of the figure. These values are used in the formula V = π∫(R(x)^2 - r(x)^2) dx to calculate the volume of revolution. Yes, the volume of revolution can be calculated for any bounded figure as long as it is rotated

Dec 12, 2006

ChaoticLlama

What is the volume of the figure bounded by y = 2x - x^2, y = 2x, x = 2, and rotated about the line y = -1.

Is this the correct integral?

[tex]\[
V = \pi \int_0^2 {((2x + 1)^2 - (2x - x^2 + 1)^2 } )dx
\]
[/tex]

Thank you for your time.

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Dec 12, 2006

chanvincent

Yes, your answer is correct.

Related to Calculating Volume of Revolution: Bounded Figure Rotated about y = -1

1. How do you calculate the volume of revolution for a bounded figure rotated about y = -1?

To calculate the volume of revolution for a bounded figure rotated about y = -1, you can use the formula V = π∫(R(x)^2 - r(x)^2) dx, where R(x) is the outer radius and r(x) is the inner radius.

2. What is the difference between outer and inner radius when calculating volume of revolution?

The outer radius is the distance from the axis of revolution to the outer edge of the figure, while the inner radius is the distance from the axis of revolution to the inner edge of the figure. These values are used in the formula V = π∫(R(x)^2 - r(x)^2) dx to calculate the volume of revolution.

3. Can the volume of revolution be calculated for any bounded figure?

Yes, the volume of revolution can be calculated for any bounded figure as long as it is rotated about a specific axis, in this case y = -1, and the outer and inner radii can be determined.

4. How does the shape of the bounded figure affect the volume of revolution?

The shape of the bounded figure can affect the volume of revolution as it determines the values of the outer and inner radii. A larger or more complex shape may result in a larger volume of revolution compared to a smaller or simpler shape.

5. Can the volume of revolution be negative?

No, the volume of revolution cannot be negative as it represents a physical volume, which cannot be negative. If the calculated value is negative, it means there was an error in the calculation or the figure was not bounded properly.