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Math Help - volume of a pyramid (not so easy)

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    volume of a pyramid (not so easy)

    Want a challenge ? Well I got one. It got me thinking for 2 days and got nothing ...

    A plane is passed parallel to the base and 8 cm from the vertex of a pyramid whose base is 45 square cm and whose altitude is 12 cm. What is the volume of that part of the pyramid after the top had been removed ?
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    Quote Originally Posted by SamanthaMathGirl View Post
    A plane is passed parallel to the base and 8 cm from the vertex of a pyramid whose base is 45 square cm and whose altitude is 12 cm. What is the volume of that part of the pyramid after the top had been removed ?
    volume of the large pyramid should be no problem, correct?

    the parallel plane cuts off a smaller similar pyramid on top whose height is 8 cm.

    since the two pyramids are similar, their respective volumes will be in the ratio \frac{8^3}{12^3}

    use the above ratio to determine the volume of the smaller pyramid ... you should be able to finish from there.
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