Question:
If a stack of 40 nickels fits snugly in the coin wrapper shown, how thick is 1 nickel? Round to the nearest hundredth.
Coin wrapper volume = 27,480 mm^3
Coin diameter = 21.18 mm
Answer:
The thickness of a coin is: 1.95mm
Step-by-step explanation:
Given
[tex]V = 27480mm^3[/tex] -- volume
[tex]d = 21.88mm[/tex] --- the diameter
Required
The thickness of each coin
This implies that, we calculate the height of each coin.
First, calculate the radius (r) of the coin
[tex]r = \frac{1}{2}d[/tex]
[tex]r = \frac{1}{2} * 21.18mm[/tex]
[tex]r = 10.59mm[/tex]
The volume of the coin is calculated as:
[tex]V =\pi r^2H[/tex]
Where H represents the total heights of the 40 coins
[tex]27480 = 3.14 * 10.58^2 * H[/tex]
Solve for H
[tex]H = \frac{27480 }{ 3.14 * 10.58^2}[/tex]
[tex]H = \frac{27480 }{ 351.480296}[/tex]
[tex]H = 78.1836145944[/tex]
The height of a coin is calculated by dividing H by 40
[tex]h = \frac{78.1836145944}{40}[/tex]
[tex]h = 1.95459036486[/tex]
[tex]h \approx 1.95mm[/tex]
Hence, the thickness of a coin is: 1.95mm
