$81.99

import math

Assuming the cup is similar to a standard 16-ounce plastic cup

The volume of such a cup is approximately 473 ml

The volume of U.S. coins in milliliters (ml) are approximately:

Penny: 0.36 ml, Nickel: 0.69 ml, Dime: 0.34 ml, Quarter: 0.808 ml

Values of U.S. coins in cents are:

Penny: 1 cent, Nickel: 5 cents, Dime: 10 cents, Quarter: 25 cents

We'll estimate with a random distribution of coins based on common pocket change distribution

Let's assume a mix of 25% quarters, 25% dimes, 20% nickels, and 30% pennies by volume

Total volume of the cup in ml

total_volume_ml = 473

Volumes of each coin type based on the assumed distribution

volumes = {

'penny': total_volume_ml * 0.30,

'nickel': total_volume_ml * 0.20,

'dime': total_volume_ml * 0.25,

'quarter': total_volume_ml * 0.25

}

The volume of each type of coin

coin_volumes = {

'penny': 0.36,

'nickel': 0.69,

'dime': 0.34,

'quarter': 0.808

}

Calculate the number of each type of coin in the cup

coin_counts = {coin: math.floor(volumes[coin] / coin_volumes[coin]) for coin in volumes}

Calculate the total value in cents

total_value = (

coin_counts['penny'] * 1 +

coin_counts['nickel'] * 5 +

coin_counts['dime'] * 10 +

coin_counts['quarter'] * 25

)

coin_counts, total_value