6.) A welder fabricates a rectangular steel tank that is \( 22^{\prime \prime} \) long, 12 " tall, and \( 13^{\prime \prime} \) wide. a) Based on these measurements what is the volume of the tank in cubic inches? b) What is the volume of the tank expressed in gallons? Use the fact that 1 gallon \( =231 \) cubic inches

To find the volume of the rectangular steel tank, we can use the formula for the volume of a rectangular prism: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \] ### a) Calculate the volume in cubic inches Given: - Length = \( 22 \, \text{inches} \) - Width = \( 13 \, \text{inches} \) - Height = \( 12 \, \text{inches} \) Now, substituting the values into the formula: \[ \text{Volume} = 22 \, \text{inches} \times 13 \, \text{inches} \times 12 \, \text{inches} \] Calculating step-by-step: 1. Calculate \( 22 \times 13 \): \[ 22 \times 13 = 286 \] 2. Now multiply by the height (12): \[ 286 \times 12 = 3432 \] Thus, the volume of the tank is: \[ \text{Volume} = 3432 \, \text{cubic inches} \] ### b) Convert the volume to gallons To convert cubic inches to gallons, we use the conversion factor \( 1 \, \text{gallon} = 231 \, \text{cubic inches} \). Now, we can convert the volume: \[ \text{Volume in gallons} = \frac{\text{Volume in cubic inches}}{231} \] Substituting the volume we calculated: \[ \text{Volume in gallons} = \frac{3432}{231} \] Calculating this gives: \[ \text{Volume in gallons} \approx 14.85 \] ### Summary of Results - a) The volume of the tank is \( 3432 \, \text{cubic inches} \). - b) The volume of the tank is approximately \( 14.85 \, \text{gallons} \).