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)
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.
To calculate the volume of a sphere, we can use the formula:
V = (4/3) * π * r^3
Given that the diameter of the tank is 5.5 feet, we can determine the radius is half that value, or 2.75 feet.
Plugging in the values into the formula, we have:
V = (4/3) * 3.14 * (2.75)^3
V = (4/3) * 3.14 * 20.796875
V ≈ 87.96502 cubic feet
Now, to convert the volume from cubic feet to gallons, we can multiply by 7.48 (the approximate number of gallons in one cubic foot):
Water volume ≈ 87.96502 * 7.48
Water volume ≈ 656.768 gallons
Therefore, the water tank holds approximately 656.768 gallons of water.
To find out how much water the tank holds, we can calculate the volume of the tank. The volume of a sphere can be found using the formula:
V = (4/3) * pi * r^3
Since the diameter of the tank is given, we need to convert it to the radius by dividing it by 2:
radius = diameter / 2
radius = 5.5 feet / 2 = 2.75 feet
Now we can substitute the value of the radius into the volume formula:
V = (4/3) * 3.14 * (2.75)^3
V = (4/3) * 3.14 * 20.036375
V ≈ 83.61872 cubic feet
To convert this volume to gallons, we can use the conversion factor given, where 1 cubic foot is about 7.48 gallons:
water in gallons = volume in cubic feet * 7.48
water in gallons ≈ 83.61872 * 7.48
water in gallons ≈ 624.27589 gallons
Therefore, the water tank holds approximately 624.28 gallons of water.