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Anonymous asked in Science & MathematicsMathematics · 2 weeks ago

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The dimensions of a prokaryotic ribosome are approximately 14 nm x 20 nm. If ribosomes occupy 20% of the volume of a bacterial cell calculate how many ribosomes are in a typical cell such as E. coli. Assume that the shape of a ribosome is approximately that of a cylinder. A typical bacterial cell volume is 1.6 um3.

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    1.6  cubic micrometers * 20% = 0.32 cubic micrometers = 0.32 * 10^(-18) cubic meters = 3.2 * 10^(-19) cubic meters

    The ribosome is a cylinder with a radius of 7 nm and a height of 20 nm

    V = pi * r^2 * h

    V = pi * (7 * 10^(-9) m)^2 * 20 * 10^(-9) m

    V = pi * 49 * 20 * 10^(-27) cubic meters

    n * V = 3.2 * 10^(-19)

    n * 49 * 20 * 10^(-27) = 3.2 * 10^(-19)

    n * 49 * 20 = 3.2 * 10^(8)

    n * 49 * 2 = 3.2 * 10^(7)

    n * 49 = 1.6 * 10^(7)

    n * 49 = 160 * 10^(5)

    n = (160/49) * 10^(5)

    n = ‭3.2653061224489795918367346938776‬.... * 10^(5)

    n = 326531, roughly

    3.3 * 10^(5) would work as well.

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