Metal Coin
Calculate the thickness of metal coin?
I have a metal sample that is 57.573 g with a density of 2.6989 g/cm^3.
If it is pounded into the shape of a coin with a diameter of 8.62 cm, how thick is the coin?
Please explain step by step, because I do not even know how to start solving this.
If we call density p, the mass m, and the volume V, then p = m/V, or density = mass divided by volume. This equation can be rearranged to V = m/p, or volume = mass divided by density.
So V = 57.573 g รท 2.6989 g/cm^3 = 21.3320 cm^3. The coin has a volume of 21.3320 cubic centimetres.
A coin is cylindrical in shape, even though its height is much smaller than the radius.
We know a cylinder has a volume equal to V = pi*h*r^2, where h is the height (or thickness) and r is the radius. The radius of any circle is half the diameter, so the radius of the coin is 4.31 cm.
So 21.3320 = pi*h*4.31^2, and dividing by 4.31^2 * pi gives
h = 21.3320/4.31^2*pi and doing this calculation gives h = 0.3655, meaining the coin is 0.3655 cm thick.
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