What is the volume of a quarter coin?

To calculate the volume of a U.S. quarter coin, we can use the formula for the volume of a cylinder because a quarter is roughly cylindrical in shape.

The formula for the volume of a cylinder is:

V=πr2h

Where:

• V is the volume,
• r is the radius of the base of the cylinder,
• h is the height (or thickness) of the cylinder,
• π is approximately 3.14159.

Step 1: Gather the dimensions of a U.S. quarter.

The standard dimensions of a U.S. quarter coin are:

• Diameter = 0.955 inches (or 24.26 mm),
• Thickness = 0.069 inches (or 1.75 mm).

Step 2: Convert the diameter to the radius.

The radius is half of the diameter, so:

• Radius r = 0.955 inches /2 =0.4775 

Step 3: Apply the formula for the volume of a cylinder.

Substitute the values for the radius and height into the formula:

V = π × (0.4775)^2 × 0.069

V = 3.14159 × 0.2278 × 0.069

V ≈ 3.14159 × 0.0157 

Step 4: Convert to cubic millimeters (optional).

To convert cubic inches to cubic millimeters (since 1 cubic inch = 16,387.064 cubic millimeters):

V ≈ 0.0493 × 16,387.064 ≈ 807.8 cubic millimeters. 

Final Answer:

The volume of a U.S. quarter coin is approximately:

• 0.0493 cubic inches, or
• 807.8 cubic millimeters.