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math

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calculate ratio of the area to volume for unit cube, a unit sphere inscribed inside the cube and as right cylinder inscribed inside the cube

  • math - ,

    sphere diameter is the side of the cube, so radius is 1/2.

    cylinder diameter and height are the side of the cube, so r = 1/2, h=1

    cube: v=1 a=6, so 6:1
    sphere: v=4/3 pi (1/2)^3 = pi/6
    a = 4pi(1/2)^2 = pi
    so, 6:1

    cylinder: v = pi (1/2)^2 = pi/4
    area= pi/2 + 2pi(1/2)(1) = 3pi/2
    so, 6:1

    whoda thunk it?

  • math - ,

    a cone is inscribed in a hemisphere which is inscribed inside a cylinder. show that the ratio of the volumes of cone to hemisphere to cylinder is 1:2:3

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