To find out how much water the spherical tank holds, we need to calculate the volume of the sphere and then convert that volume from cubic feet to gallons.
- First, we need the radius of the sphere. The diameter is given as 5.5 feet, so the radius \( r \) is half of that:
\[ r = \frac{5.5}{2} = 2.75 \text{ feet} \]
- The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (2.75)^3 \]
- Now, calculate \( (2.75)^3 \):
\[ (2.75)^3 = 2.75 \times 2.75 \times 2.75 = 20.796875 \text{ cubic feet} \]
- Now substituting back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 20.796875 \]
Calculating this step by step:
\[ \frac{4}{3} \times 3.14 \approx 4.18666667 \] \[ V \approx 4.18666667 \times 20.796875 \approx 87.0554451 \text{ cubic feet} \]
- Now, to convert cubic feet to gallons, we use the conversion factor \( 1 \text{ cubic foot} \approx 7.48 \text{ gallons} \):
\[ \text{Gallons} = 87.0554451 \times 7.48 \approx 651.3 \text{ gallons} \]
Therefore, the tank holds approximately 651.3 gallons.
The answer is: 651.3 gallons.