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:
[tex]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[/tex]
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:
[tex]V=\pi r^2h\\r = \sqrt \frac{V}{\pi h}= \sqrt\frac{1.121 cm^3}{\pi \times 0.2cm}=1.336 cm[/tex]
Finally, we know that the diameter is twice the radius, therefore the diameter of each coin is 2.67 cm.
The Diameter of each coin is 2.67 cm.
Given that, Kim has 0.12 cubic meters of silver which she needs to make into [tex]1.07*10^{5}[/tex] coins of thickness 2 mm.
Total volume of silver material [tex]=0.12m^{3}[/tex]
Thickness of coin (h) [tex]=2mm=2*10^{-3} m[/tex]
Since, the coins are made in cylindrical shape.
Let us consider that radius of each coin is r .
Volume of each coin [tex]=\pi r^{2}h[/tex] and value of [tex]\pi=3.14[/tex]
Volume of [tex]1.07*10^{5}[/tex] coins,
[tex]V=1.07*10^{5}* \pi*r^{2}*h \\\\0.12=1.07*10^{5}*3.14*r^{2}*2*10^{-3} \\\\r^{2}=\frac{0.12}{1.07*10^{5} *3.14*2*10^{-3} } \\\\r^{2}=1.785*10^{-4}\\\\r=\sqrt{1.785*10^{-4}} =0.01336m[/tex]
We know that, 1 meter = 100 cm.
[tex]r=0.01336*100=1.336cm[/tex]
Since, diameter is two times of radius.
So that, Diameter of each coin is,
[tex]=2*1.336=2.67cm[/tex]
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