geometry

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If the ratio of the volume of two similar solids is 8:125, then what is the ratio of their surface areas?

  • geometry -

    lets take a rectangular solid, in the form of a long prism.

    V=bhl
    Area= 2(bh+lh+bl)

    let l= 8, b=8h
    so, for v=8, l=8, b,h=1
    now scale it up to 125/8
    l=8*cubrt(125/8)=8*5/2=40
    b= 5/2 h=5/2
    original surface area: 2(1+8+8)=34
    new surface area: 2(25/4+200/2+200/2)
    = 2(412.5/2)=412.3

    ratios of surefce area 34:412.3

    Now you need to figure other shapes. Try a cube, and a sphere.

  • geometry -

    If two solids have volume ratio r^3, then

    their linear ratio (sides length) is r
    their area ratio (surface area) is r^2

    So, since
    v/V = (2/5)^3
    a/A = (2/5)^2 = 4/25

    You gained a factor of 2 there when you said 8*5/2 = 40

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