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19 March, 03:44

Rosario draws the right triangular prism shown here and calculates the volume. She then draws a second right triangular prism in which the dimensions are tripled. What is the relationship between the volumes of the two prisms?

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  1. 19 March, 05:03
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    The volume of the original prism is given by:

    V1 = (1/2) * (b) * (h) * (H)

    Where,

    b: base of the triangle

    h: height of the triangle

    H: prism height

    The volume of the prism with new dimensions is:

    V2 = (1/2) * (3b) * (3h) * (3H)

    Rewriting:

    V2 = (3 * 3 * 3) * (1/2) * (b) * (h) * (H)

    V2 = (27) * (1/2) * (b) * (h) * (H)

    V2 = (27) * V1

    Answer:

    The relationship between the volumes of the two prisms is:

    V2 = (27) * V1
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