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March 24, 2017

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The surface area of a rectangular prism is 10.4 in2. What is the surface area of a similar prism that is larger by a scale factor of 3?

I am tearing my hair out over this question! Please help asap!

  • Math - ,

    The surface areas of similar solids is proportional to the square of their sides
    since the ratio of sides is 1 : 3
    their surface areas have the ratio 1^2 : 3^2 or 1 : 9
    so the surface area is 9(10.4) or 93.6

    or

    original width = x
    original length = y
    original heigt = z
    original surface area = 2(xy) + 2(xz) + 2(yz)
    = 2(xy + xz + yz)

    new width = 3x
    new length = 3y
    new height = 3z
    new surface area = 2(9xy) + 2(9xz) + 2(9yz)
    = 18(xy + xz + yz)

    ratio of new to old = 18(xy + xz + yz) : 2(xy + xz + yz)
    = 9 : 1

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