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Answer:
The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.
Step-by-step explanation:
A nickel can be modelled by the formula of a right cylinder, the approximate volume of the stack of nickels ([tex]V_{net}[/tex]), measured in cubic milimeters, is the product of the number of elements ([tex]n[/tex]), no unit, and the volume of each element ([tex]V[/tex]), measured in cubic milimeters. That is:
[tex]V_{net} = n\cdot V[/tex] (1)
By volume equation of right cylinder, we have the following formula:
[tex]V_{net} = \frac{\pi}{4}\cdot n \cdot D^{2}\cdot h[/tex] (2)
Where:
[tex]n[/tex] - Amount of nickels, no unit.
[tex]D[/tex] - Diameter of nickel, measured in milimeters.
[tex]h[/tex] - Thickness of nickel, measured in milimeters.
If we know that [tex]n = 40[/tex], [tex]D = 20\,mm[/tex] and [tex]h = 2\,mm[/tex], then the net volume of the stack of nickels is:
[tex]V_{net} = \frac{\pi}{4}\cdot (40)\cdot (20\,mm)^{2}\cdot (2\,mm)[/tex]
[tex]V_{net} \approx 25132.741\,mm^{3}[/tex]
The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.