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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

User BoSkiv
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Answer:

The diameter of each coin is approximately 2.778 centimeters.

Explanation:

According to the statement, 0.12 cubic meters (
1.20* 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) = (1.20* 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) = (\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) = (4\cdot V_(c))/(\pi\cdot h)


D = 2\cdot \sqrt{(V_(c))/(\pi\cdot h) }


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


D \approx 27.779\,mm

The diameter of each coin is approximately 2.778 centimeters.

User Leann
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