To find the volume of a roll of quarters valued at $10, we first need to determine the number of quarters in the roll and then calculate the total volume they occupy.
1. The value of a single quarter is $0.25 (25 cents).
2. To calculate the number of quarters in a $10 roll, divide $10 by $0.25:
$10 / $0.25 = 40 quarters in the roll.
Now, to find the total volume of the roll of quarters, we need to consider the volume of a single quarter and then multiply it by the total number of quarters in the roll.
3. The volume of a quarter can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius (half of the diameter) and h is the height (thickness) of the quarter.
Given that the diameter is 24.26 mm (so the radius, r = 12.13 mm) and the height is 1.75 mm, we can plug these values into the formula:
V = π(12.13)^2 * 1.75 ≈ 809 mm³ (rounded to the nearest cubic millimeter).
4. Finally, to find the total volume of the roll of quarters, multiply the volume of a single quarter by the total number of quarters in the roll:
Total volume = 809 mm³ * 40 = 32,360 mm³.
Therefore, the closest option to the calculated total volume is approximately 32,360 mm³, which would be rounded to 32,357 mm³.
