How to find the volume of a coin.?

February 4th, 2010 | by admin |

A Coin dealer offers to sell you an ancient gold coin that is 2.2 cm in diameter and 3.0 mm in thickness. The density of gold is 19.3g/cm^3. How much should the coin weigh if it is pure gold?

I believe I would start my conversion with 19.3g/cm^3 but wouldn’t I have to calculate the volume. How does one calculate the volume of a coin? Please show the problem in steps, trying to learn.

A coin is a cylinder with a large diameter and a small height. The volume of a cylinder can be calculated by multiplying the are of the circle by the height. I am sure you know the formula for the area of a circle? So that’ll give you the volume. The density is just the weight that one cm^3 would weigh. Once you’ve got the actual volume of the coin, multiply by the density and you’re there.

Alternatively, drop the coin into a full (!!) glass of water and measure the volume of water that overflows. That’ll be the volume of the coin.

  1. 3 Responses to “How to find the volume of a coin.?”

  2. By André on Feb 4, 2010 | Reply

    A coin is a cylinder with a large diameter and a small height. The volume of a cylinder can be calculated by multiplying the are of the circle by the height. I am sure you know the formula for the area of a circle? So that’ll give you the volume. The density is just the weight that one cm^3 would weigh. Once you’ve got the actual volume of the coin, multiply by the density and you’re there.

    Alternatively, drop the coin into a full (!!) glass of water and measure the volume of water that overflows. That’ll be the volume of the coin.
    References :

  3. By captainservo on Feb 4, 2010 | Reply

    The volume of the coin is a a very short cylinder. The volume of a cylinder is Pi X Radius^2 x Height.
    The coin’s radius is equal to 1/2 the diameter, and the height is the thickness (but make sure the units are the same).

    3.14 x 1.1^2 x 0.3 = 1.1 cm^3

    The coin should weigh 21 grams
    References :

  4. By Tim on Feb 4, 2010 | Reply

    You’re given the dimensions of the coin. Treat it as a cylinder.
    v=pi.r^2.h
    v= 3.14x(1.1^2)x0.3
    v=1.14cm^3

    now density = mass/volume
    so rearrange the formula to:
    mass= density x volume
    mass = 19.3 x 1.14
    mass = 22.0g

    Hope this helps :)
    References :

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