Questions: A nickel is found to have a volume of 2.81 * 10^4 liters. Show, using unit analysis, what the volume of the nickel is in quarts.

Solution Steps

The given volume of the nickel is \(2.81 \times 10^4\) liters.

We need to convert liters to quarts. The conversion factor between liters and gallons is given as: \[ 3.79 \, \text{L} = 1 \, \text{gal} \]

We also know that: \[ 1 \, \text{gal} = 4 \, \text{qt} \]

First, convert the volume from liters to gallons: \[ 2.81 \times 10^4 \, \text{L} \times \frac{1 \, \text{gal}}{3.79 \, \text{L}} \]

Next, convert the volume from gallons to quarts: \[ \left( 2.81 \times 10^4 \, \text{L} \times \frac{1 \, \text{gal}}{3.79 \, \text{L}} \right) \times \frac{4 \, \text{qt}}{1 \, \text{gal}} \]

Combine the conversion factors and perform the calculation: \[ 2.81 \times 10^4 \times \frac{4}{3.79} \]

\[ = 2.81 \times 10^4 \times 1.0554 \]

\[ = 2.9667 \times 10^4 \, \text{qt} \]

Final Answer