Question

Suppose your metal sample is hammered into the shape of a thin coin with a diameter of 8.62 cm. Determine the thickness (in mm) of this metal sheet. Use the measured metal mass and true denisty of your metal for this calculation.
measured metal mass: 83.956 g
true density: 8.90 g/cm3

Answer 1

Answer:

The thickness of the metal sheet is 0.162 centimeters.

Explanation:

If mass within the coin is uniformly distributed, then the density ($\rho$), measured in grams per cubic centimeter, can be represented by the following formula:

$\rho = \frac{m}{\frac{\pi}{4}\cdot D^{2}\cdot z }$ (1)

Where:

$m$ - Mass, measured in grams.

$D$ - Diameter, measured in centimeters.

$z$ - Thickness, measured in centimeters.

If we know that $m = 83.956\,g$, $D = 8.62\,cm$ and $\rho = 8.90\,\frac{g}{cm^{3}}$, then the thickness of the coin is:

$z = \frac{m}{\frac{\pi}{4}\cdot D^{2}\cdot \rho }$

$z = \frac{83.956\,g}{\frac{\pi}{4}\cdot (8.62\,cm)^{2}\cdot \left(8.90\,\frac{g}{cm^{3}} \right) }$

$z = 0.162\,cm$

The thickness of the metal sheet is 0.162 centimeters.