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A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

  • math -

    v = 1/3 * s^2 * h
    multiply dimensions by 5:
    V = 1/3 * (5s)^2 * (5h)
    = 1/3 * 25s^2 * 5h
    = 1/3 *25s^2 * 5h
    = 125 * 1/3 * s^2 * h
    = 125v

    multiplying the dimensions of a figure by k causes

    length to multiply by k
    area by k^2
    volume by k^3

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