A technician is inspecting a fire sprinkler system. The water tank is 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)
The radius of the water tank is half of the diameter, so the radius is 5.5 ft / 2 = <<5.5/2=2.75>>2.75 ft.
The formula for the volume of a sphere is volume = (4/3) * pi * radius^3.
Using the given value of pi as 3.14, the volume of the water tank is (4/3) * 3.14 * 2.75^3 = 79.5635 cubic feet.
To convert to gallons, multiply by 7.48: 79.5635 cubic feet * 7.48 gallons/cubic foot = 594.43222 gallons.
Therefore, the water tank holds approximately 594 gallons.
To find the volume of the water tank, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that the diameter of the sphere is 5.5 feet, we can find the radius by dividing the diameter by 2:
r = d/2 = 5.5/2 = 2.75 feet
Substituting the radius into the volume formula:
V = (4/3) * π * (2.75)^3
V = (4/3) * 3.14 * (2.75)^3
V ≈ 4.19 * 19.12
V ≈ 80.15 cubic feet
Now, to convert the volume to gallons, we can use the conversion factor given, which is 7.48 gallons per cubic foot:
Water tank capacity = V * 7.48
Water tank capacity ≈ 80.15 * 7.48
Water tank capacity ≈ 598.15 gallons
Therefore, the water tank holds approximately 598.15 gallons of water.
To find the volume of the water tank, you can use the formula for the volume of a sphere:
Volume = (4/3) * π * r^3
Given that the diameter of the water tank is 5.5 feet, we can find the radius by dividing the diameter by 2:
Radius = 5.5 feet / 2 = 2.75 feet
Now we can substitute the value of the radius into the volume formula:
Volume = (4/3) * 3.14 * (2.75 feet)^3
Calculating this, we get:
Volume = (4/3) * 3.14 * 20.796875 feet^3
Simplifying further:
Volume ≈ 87.9647 feet^3
Since there are about 7.48 gallons in one cubic foot, we can calculate the amount of water the tank holds by multiplying the volume by the conversion factor:
Amount of water = 87.9647 feet^3 * 7.48 gallons/foot^3
Calculating this, we get:
Amount of water ≈ 657.251 gallons
So, the spherical water tank holds approximately 657.251 gallons of water.