A rectangular water storage tank measures 45 inches by 52 inches by 23 inches. Find, to the nearest hundredth, the gallon capacity of the tank. Round to the nearest hundredth 1 gallon \( =231 \) cubic inches

To find the volume of the tank, we first calculate the volume in cubic inches by using the formula for the volume of a rectangular prism: \( V = length \times width \times height \). So, substituting in our dimensions: \( V = 45 \, \text{in} \times 52 \, \text{in} \times 23 \, \text{in} = 52,350 \, \text{cubic inches} \). Now, to convert cubic inches to gallons, we use the conversion factor \(1 \, \text{gallon} = 231 \, \text{cubic inches}\): \( \text{Gallons} = \frac{52,350 \, \text{cubic inches}}{231 \, \text{cubic inches/gallon}} \approx 226.14 \, \text{gallons} \). Therefore, the capacity of the tank is approximately 226.14 gallons. If you're ever puzzled about conversions, remember that breaking the problem into steps can help! Many people make the mistake of forgetting to use the conversion ratio correctly or mixing up the units. Double-checking your work, especially with units, can save you from a simple slip! Always keep a handy conversion chart or calculator nearby for tricky conversions! Enjoy learning more about the applications of volume calculations in everyday life! For instance, engineers and architects frequently need to calculate water capacity to ensure structures are up to code for drainage and potential overflow situations. This knowledge helps prevent flooding and ensures efficient water management in urban planning.