6 A swimming pool is shaped like a rectangular prism. The bottom of the pool has an area of \( 48 \mathrm{ft}^{2} \) and the pool is \( 5 \frac{1}{2} \mathrm{ft} \) deep. What is the volume of the water in the pool when it is full?

To find the volume of the water in the swimming pool, we can use the formula for the volume of a rectangular prism, which is given by: \[ V = A \times h \] where: - \( V \) is the volume, - \( A \) is the area of the base, - \( h \) is the height (or depth in this case). ### Step 1: Identify the known values - The area of the bottom of the pool, \( A = 48 \, \text{ft}^2 \) - The depth of the pool, \( h = 5 \frac{1}{2} \, \text{ft} \) ### Step 2: Convert the mixed number to an improper fraction The depth \( h = 5 \frac{1}{2} \) can be converted to an improper fraction: \[ h = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \, \text{ft} \] ### Step 3: Calculate the volume Now we can substitute the values into the volume formula: \[ V = A \times h = 48 \, \text{ft}^2 \times \frac{11}{2} \, \text{ft} \] ### Step 4: Perform the multiplication Calculating the volume: \[ V = 48 \times \frac{11}{2} = \frac{48 \times 11}{2} = \frac{528}{2} = 264 \, \text{ft}^3 \] ### Final Answer The volume of the water in the pool when it is full is \( 264 \, \text{ft}^3 \).