Geometry

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what are the dimensions of two cylinders where the first cylinder has a greater surface area and the second cylinder has a greater volume?

  • Geometry -

    There are an infinite number of possibilities. You need to provide more information, if you want a unique answer.

  • Geometry -

    let the height be h, and the radius be r
    Volume = πr^2h
    Surface area = 2πr^2 + 2πrh

    volume > SA
    πr^2h > 2πr^2 + 2πrh, divide by πr
    rh > 2r + 2h
    rh - 2h > 2r
    h > 2r/(r-2)

    if SA > volume
    then h < 2r/(r-2)

    for both to be true,
    h = 2r/(r-2)

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