Question

0.12 cubic meters of silver which she needs to make into 9.9e4 coins of thickness 2 mm. If she uses all of the silver, what is the diameter in centimeters of each coin

Answer 1

Answer:

The diameter of each coin is approximately 2.778 centimeters.

Step-by-step explanation:

According to the statement, 0.12 cubic meters ($1.20\times 10^{8}\,mm^{3}$) were used to produce 99000 coins. First, we calculate the volume of each coin ($V_{c}$), measured in cubic meters, by dividing the total volume by the number of coins. That is:

$V_{c} = \frac{1.20\times 10^{8}\,mm^{3}}{99000}$

$V_{c} =1212.121\,mm^{3}$

Then, diameter ($D$), measured in milimeters, can be derived from the following volume formula:

$V_{c} = \frac{\pi}{4}\cdot D^{2}\cdot h$ (1)

Where $h$ is the thickness of the coin, measured in milimeters.

If we know that $h = 2\,mm$ and $V_{c} =1212.121\,mm^{3}$, then the diameter of each coin is:

$D^{2} = \frac{4\cdot V_{c}}{\pi\cdot h}$

$D = 2\cdot \sqrt{\frac{V_{c}}{\pi\cdot h} }$

$D = 2\cdot\sqrt{\frac{1212.121\,mm^{3}}{\pi\cdot (2\,mm)} }$

$D \approx 27.779\,mm$

The diameter of each coin is approximately 2.778 centimeters.