Question

Kim has a metal casting company which makes commemorative coins. She has 0.12 cubic meters of silver which she needs to make into 1.07e5 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 coin has a diameter of 2.67 cm

Explanation:

First, we need to find the volume of each coin by dividing the total volume of silver by the number of coins. We have also to do a conversion of units in terms of centimeters as follows:

$V=0.12 m^3\times (\frac{100cm}{1m})^3=12000\ cm^3\\V_c=\frac{120000\ cm^3}{1.07\times10^5}= 1.121 cm^3$

Then, we define the coin as a tiny cilinder to determine its diameter. In that order we use the cilinder's volumen equation as follows:

$V=\pi r^2h\\r = \sqrt \frac{V}{\pi h}= \sqrt\frac{1.121 cm^3}{\pi \times 0.2cm}=1.336 cm$

Finally, we know that the diameter is twice the radius, therefore the diameter of each coin is 2.67 cm.