A technician is inspecting a fire sprinkler system. The water tank spherical with a diameter of 5.5 feet. How much water does the tank hold ? (One cubic foot is about 7.48 gallons. Use 3.14 for pi)

Answer 1

To find the volume of the water tank, we need to calculate the volume of a sphere using the formula:

\[ V = \frac{4}{3} \pi r^3 \]

Given that the diameter of the sphere is 5.5 feet, we can calculate its radius by dividing the diameter by 2:

\[ r = \frac{5.5 \text{ feet}}{2} = 2.75 \text{ feet} \]

Substituting this value into the formula, we have:

\[ V = \frac{4}{3} \times 3.14 \times (2.75 \text{ feet})^3 \]

Simplifying:

\[ V = \frac{4 \times 3.14 \times 2.75^3}{3} \]

Calculating the volume:

\[ V \approx 71.625 \text{ cubic feet} \]

Now, to convert the volume to gallons, we multiply by 7.48:

\[ \text{Water Tank Capacity} = 71.625 \text{ cubic feet} \times 7.48 \text{ gallons/cubic foot} \]

Calculating:

\[ \text{Water Tank Capacity} \approx 535.11 \text{ gallons} \]

Therefore, the water tank holds approximately 535.11 gallons.