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Math Help - Help with area and volume problems part 2

  1. #1
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    Help with area and volume problems part 2

    Ok, here are a couple of the other problems i need help with:

    A cylindrical hole is drilled through the center of a sphere of radius R. Use the method of cylindrical shells to find the volume of the remaining solid, given that the solid is 6 cm high.

    Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y=-x^2 +4x -3 and y=0
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  2. #2
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    Quote Originally Posted by Missylovesmathz View Post
    Ok, here are a couple of the other problems i need help with:

    A cylindrical hole is drilled through the center of a sphere of radius R. Use the method of cylindrical shells to find the volume of the remaining solid, given that the solid is 6 cm high.
    This is not enough information. Check to make sure you copied it properly. Is the hole drilled vertically? Do we know anything else?

    Quote Originally Posted by Missylovesmathz View Post
    Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y=-x^2 +4x -3 and y=0
    I learned this under the name "bundt cake method." Your teacher/textbook may have a different name. But, the solid looks like a cake. Surely you've covered an example, otherwise you wouldn't be asked to solve such a problem?
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    Actually, I think it is enough information on the hole-drilling problem. We know the radius of the sphere, and we know that the drilled hole went through the center. You can orient the object any way you want. I'd probably put the center of the sphere at the origin, and orient the hole to be on the y-axis. Then you use the shell method as described. I suppose you don't technically know that R<3 cm, but you could infer that through the use of the "through" language.
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    Quote Originally Posted by Ackbeet View Post
    Actually, I think it is enough information on the hole-drilling problem. We know the radius of the sphere, and we know that the drilled hole went through the center. You can orient the object any way you want. I'd probably put the center of the sphere at the origin, and orient the hole to be on the y-axis. Then you use the shell method as described. I suppose you don't technically know that R<3 cm, but you could infer that through the use of the "through" language.
    Seems to me that assumes we measure height in the same direction as the axis of the hole. Suppose we measure height in a perpendicular direction, then the height is simply the diameter of the sphere, and we have no information on the radius of the hole.
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    Oh, you're right. My bad. I thought the 6 cm referred to the sphere, which it really ought to.
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