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Math Help - Volume of a pyramid

  1. #1
    VkL
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    Volume of a pyramid



    --> Volume = \lim \Delta y \rightarrow \infty  \sum s^2 \Delta y

    How do you proceed from there?
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  2. #2
    Eater of Worlds
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    If s is the length of a side of the slice and h is the height of the pyramid, then by similar triangles:

    \frac{\frac{1}{2}s}{\frac{1}{2}a}=\frac{h-y}{h}

    or s=\frac{a}{h}(h-y)

    The area, A(y), of the cross section at y is:

    A(y)=s^{2}=\frac{a^{2}}{h^{2}}(h-y)^{2}

    Therefore, the volume is:

    \int_{0}^{h}A(y)dy=\frac{a^{2}}{h^{2}}\int_{0}^{h}  (h-y)^{2}dy

    Using a=2, perform the integration and you should get \frac{1}{3}(2)^{2}h
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  3. #3
    VkL
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    I got 8/3
    I did every thing correct though
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