Anonymous asked in Science & MathematicsChemistry · 4 months ago

A metal ball-bearing with a circumference of 43.1 mm weighs 12.1 g. What is the density of the metal in g/cm3?

1 Answer

  • 4 months ago
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    The formula for the circumference of a sphere is the same as the formula for the circumference of a circle, since a circle is what you get when you bisect a sphere through it's center: 2πr, where r is the radius.

    Solve this equation (C = 2πr) for the radius in terms of the circumference:

    r = C/2π

    The formula for the volume of a sphere is (4/3)πr^3. Substitute the expression equal to r (found above) in order to find the volume in terms of the circumference:

    V = (4/3)π(C/(2π))^3 = C^3/(6 π^2)

    Then substitute the given value for the circumference to determine the volume:

    (43.1 mm)^3) / (6 π^2) = 1352.01 mm^3 = 1.35201 cm^3

    (12.1 g) / (1.35201 cm^3) = 8.95 g/cm^3

    [You didn't ask, but the common metal with a density like that is copper.]

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