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Math Help - Find the volume of the solid Question

  1. #1
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    Find the volume of the solid Question

    I do not know how to do these problem should some one help

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

    y=x^6, y=1; about y=2

    ________
    and

    You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=3900 and a square base with side s=1470. To impress your Egyptian subjects, find the volume of the pyramid.

    ___________
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by killasnake View Post
    I do not know how to do these problem should some one help
    You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=3900 and a square base with side s=1470. To impress your Egyptian subjects, find the volume of the pyramid.

    ___________
    A pyramid's volume is: V=\frac{1}{3}Ah

    where: A=\text{Area of the Base}

    And: h=\text{The Height of the Pyramid}

    So the area of the base is obviously A=s^2=1470^2=2160900

    So then find the volume
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  3. #3
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    Thank you for the help Quick, Any ideas how to do the first one?
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  4. #4
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    Hello, killasnake!

    I must assume that you know about Volumes of Revolution . . .


    Find the volume of the solid obtained by rotating the region bounded by:
    . . y = x^6,\;y=1, about y=2
    Code:
                      |
                     2|
          - - - - - - + - - - - - -
                      |
                      |
           *- - - - - + - - - - -*(1,1)
             *::::::::|::::::::*
                *:::::|:::::*
          - - - - - - * - - - - - - -
                      |

    V \;=\;2 \times \int^1_0\left[(2-x^6)^2 - (2 - 1)^2\right]\,dx

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