To determine how many gallons of water are needed to fill the rectangular pool to 85% capacity, we first need to calculate the volume of the pool in cubic feet, and then convert that volume to gallons.
The dimensions of the pool are:
- Length = 29 feet
- Width = 11 feet
- Depth = 4 feet
The volume \( V \) of the pool in cubic feet can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{Length} \times \text{Width} \times \text{Depth} \]
Substituting the values:
\[ V = 29 , \text{ft} \times 11 , \text{ft} \times 4 , \text{ft} \]
Now calculating that:
\[ V = 29 \times 11 = 319 , \text{ft}^2 \] \[ V = 319 \times 4 = 1276 , \text{ft}^3 \]
Next, we need to find out the volume needed for 85% capacity:
\[ \text{Volume at 85%} = 0.85 \times 1276 , \text{ft}^3 = 1084.6 , \text{ft}^3 \]
Now, we convert cubic feet to gallons using the conversion factor of 7.48 gallons per cubic foot:
\[ \text{Gallons} = 1084.6 , \text{ft}^3 \times 7.48 , \text{gallons/ft}^3 \] \[ \text{Gallons} \approx 8128.468 , \text{gallons} \]
Rounding to the nearest whole number, the pool would require approximately:
\[ \text{About } 8128 \text{ gallons of water.} \]