Currently my class it calculating volumes of solids by rotating them

In summary, the conversation discusses the process of calculating volumes of solids by rotating them around an axis, using the example of the function f(x) = x^2 bounded by s = { (x,y) | 0≤x≤1 , 0≤y≤1} and rotating it around the y-axis. The speaker expresses difficulty visualizing the solid and asks if there is software available to create 3D images. They mention a CAD program as a potential solution.
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Miike012
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Currently my class it calculating volumes of solids by rotating them about some axis, say for instance the function f(x) = x^2 bounded by s = { (x,y) | 0≤x≤1 , 0≤y≤1} and rotating it about the y - axis. I understand the general look of the graph on paper but I can't visualize the actual solid, for instance is it solid all the way through? or is it hallow? anyways.. is there software that can draw 3d pics so I can see what the figure looks like?
 
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That there might help you a bit.

I know its a CAD program but you might pick up what's going on it.

 
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FAQ: Currently my class it calculating volumes of solids by rotating them

1. How do you calculate the volume of a solid by rotating it?

The volume of a solid can be calculated by first finding its cross-sectional area, then multiplying that by the distance the solid is rotated. This method is known as the disk/washer method.

2. Can you give an example of using the disk/washer method to calculate volume?

For example, if we have a solid with a circular cross-section, we can find the area of the circle by using the formula A = πr^2, where r is the radius of the circle. Then, if we rotate this solid around an axis, we can multiply the cross-sectional area by the distance the solid is rotated to find the volume.

3. What is the difference between the disk/washer method and the shell method?

The disk/washer method is used when the cross-section of the solid is perpendicular to the axis of rotation, while the shell method is used when the cross-section is parallel to the axis of rotation. The shell method involves finding the circumference of the solid and multiplying it by the height of the solid.

4. How do you know which method to use when calculating volume of a solid?

You can determine which method to use based on the shape of the cross-section of the solid and the axis of rotation. If the cross-section is perpendicular to the axis, use the disk/washer method. If the cross-section is parallel to the axis, use the shell method.

5. Are there any other methods for calculating volume of solids?

Yes, there are other methods such as the cylindrical shell method, the method of slicing, and the triple integral method which can be used for more complex shapes. These methods involve breaking down the solid into smaller parts and using different integration techniques to find the volume.

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