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March 30, 2017

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

  • Science - ,

    Let the unit cube side be a. Its volume is a^3. Its area is 6a^2. The ratio is a/6.

    The inscribed sphere has a volume of (pi/6)a^3 and an area of pi*(a/2)^2*4 = pi a^2. The ratio is a/6.

    The inscribed right cylinder has a volume (pi/4)a^2*a = pi*a^3/4 and an area a*pi*a + 2 pi (a/2)^2
    = (3/2) pi a^2
    The ratio is a/6.

    Interesting result

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