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Math Help - Calculus Worded Problem Help

  1. #1
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    Calculus Worded Problem Help

    A rectangular block is such that the sides of its base are of length x cm and 3x cm. The
    sum of the lengths of all its edges is 20 cm.

    a) Show that the volume, V cm^3, is given by V = 15x^2 − 12x^3.

    I get that V = L*W*H

    However, I cannot visualise this "rectangular block". Can someone show me what this block looks like?
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  2. #2
    Super Member Gamma's Avatar
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    Iowa City, IA
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    looks like a shoe box. Rectangular prism.

    So you know that the base is a rectangle, but there are two bases (the bottom and top of the box if you will) and 4 edges that would represent the height of this box.

    So you just need to figure out what that height is. You know that the sum of all the edges is 20 cm, and this is sufficient to determine the dimensions of this box.

    you know that the perimeter of the base 2(x+3x)=8x cm, but there are two of these, the top and bottom, so that yields 16x cm. Now you need to account for these 4 vertical edges, the height, so call it h.

    Then we have 16x+4h=20 \Rightarrow h=\frac{20-16x}{4}=5-4x.

    Now to calculate your volume, you just need to use your formula.

    V=LWH=(x)(3x)(5-4x)=15x^2-12x^3 as desired.
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