Chemistry Quarter Thickness in mm

Question

A quarter is a coin that contains 91.6% by mass copper and 8.33 % by mass nickel. It has a diameter of

0.955 inches and density of 7.01 g/cm3. If a single quarter contains 0.183 ounces of copper, what is the

thickness of a quarter, in millimeters?

Answer 1

Think of the quarter as a cylinder with a diameter of 0.955 inches and the height is unknown, because this is what the question is asking us to determine. So, we begin with the formula for finding the volume of a cylinder

V = π r² h

Before we can effectively use this to help solve the problem, there are several preliminary calculations that need to be performed so that we can get all of the variables in this equation (V, r, and h) into units that are suitable and in agreement with each other. We will begin with r, the radius of the coin and convert it to cm units.

radius = r = diameter / 2 = 0.955 inches / 2 = 0.4775 inches x 2.54 cm / inch = 1.21 cm = r

Next we will have to calculate the mass of the coin in grams, because we will use that to find the volume (V) of the coin, since volume = mass / density (and we know the density, so need to find the mass).

mass = mass of copper + mass of nickel and copper is 91.6% of total mass, so total mass can be found as..

mass = 0.183 oz / x = 91.6% / 100% and x = 0.1998 ounces total mass x 28.35 g / oz = 5.66 g

Now for the volume:

V = mass / density = 5.66 g / 7.01 g / cm³ = 0.807 cm³ = Volume (V)

Finally, we can now use the formula for volume of a cylinder to solve for h (height)...

V = π r² h = 0.807 cm³ = (3.14)(1.21 cm)²(h cm)

h = height = 0.807 cm³ / (3.14)(1.21 cm)²

h = 0.176 cm

Converting this height in cm to height in millimeters, we have...

0.176 cm x 10 mm / cm = 1.76 mm (Answer)