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18 October, 03:13

A sporting goods company sells a tent with the dimensions shown. The company wants to introduce a new, larger tent that is geometrically similar to the original tent but with a height of 6 feet. How will the volume of the new tent compare with the volume of the original tent?

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  1. 18 October, 03:24
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    The volume of the new tent will be 3/2 times the volume of the original

    Step-by-step explanation:

    The original tent is a triangular prism, which missing dimensions of the tent are:

    base (b) : 6 ft height (h) : 4 ft length (l) : 7 ft

    Volume of the original tent:

    V = 1/2*b*h*l

    The only difference between the new and the original tent are their heights. Let's call h' = 6 ft to the height of the new tent.

    Volume of the new tent:

    V' = 1/2*b*h'*l

    Dividing V' by V:

    V'/V = (1/2*b*h'*l) / (1/2*b*h*l)

    V'/V = h'/h

    Replacing with dа ta:

    V'/V = 6/4

    V' = 3/2*V
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