What is the weight in pounds of a gold bar 12.0 inches long, 6.00 inches wide and 3.00 inches thick? The density of gold is `19.3gcm^(-3)`. Given 1 inch = 2.54 cm, 1lb = 453.6 g.

Explanation

To find the weight of the gold bar in pounds, we will follow these steps:

### Step 1: Calculate the Volume of the Gold Bar
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{thickness} \]
Given:
- Length = 12.0 inches
- Width = 6.00 inches
- Thickness = 3.00 inches

Substituting the values:
\[ V = 12.0 \, \text{inches} \times 6.00 \, \text{inches} \times 3.00 \, \text{inches} \]
Calculating the volume:
\[ V = 216.0 \, \text{inches}^3 \]

### Step 2: Convert Volume from Cubic Inches to Cubic Centimeters
Since the density of gold is given in grams per cubic centimeter, we need to convert the volume from cubic inches to cubic centimeters. We know that:
\[ 1 \, \text{inch} = 2.54 \, \text{cm} \]
Thus,
\[ 1 \, \text{inch}^3 = (2.54 \, \text{cm})^3 = 16.387 \, \text{cm}^3 \]
Now, converting the volume:
\[ V = 216.0 \, \text{inches}^3 \times 16.387 \, \text{cm}^3/\text{inch}^3 \]
Calculating:
\[ V \approx 3537.432 \, \text{cm}^3 \]

### Step 3: Calculate the Mass of the Gold Bar
Using the density of gold, which is \( 19.3 \, \text{g/cm}^3 \), we can find the mass \( m \) using the formula:
\[ m = \text{density} \times \text{volume} \]
Substituting the values:
\[ m = 19.3 \, \text{g/cm}^3 \times 3537.432 \, \text{cm}^3 \]
Calculating the mass:
\[ m \approx 68,309.46 \, \text{g} \]

### Step 4: Convert Mass from Grams to Pounds
To convert grams to pounds, we use the conversion factor:
\[ 1 \, \text{lb} = 453.6 \, \text{g} \]
Thus,
\[ \text{Weight in pounds} = \frac{m}{453.6 \, \text{g/lb}} = \frac{68,309.46 \, \text{g}}{453.6 \, \text{g/lb}} \]
Calculating the weight in pounds:
\[ \text{Weight in pounds} \approx 150.6 \, \text{lb} \]

### Final Answer
The weight of the gold bar is approximately **150.6 pounds**.

---