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.)
Formula Sheet
*
1 point
651.3 gallons
696.6 gallons
710.4 gallons
976.9 gallons
To find the volume of a spherical tank, we can use the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Given the diameter of 5.5 feet, we can find the radius by dividing the diameter by 2:
radius = diameter / 2 = 5.5 ft / 2 = 2.75 ft
Now, we can substitute the values into the formula to find the volume:
V = (4/3) * 3.14 * (2.75 ft)^3
V ≈ 4.19 * (2.75 ft)^3
V ≈ 4.19 * 20.796875 ft^3
V ≈ 87.16 ft^3
To convert the volume from cubic feet to gallons, we can multiply by the conversion factor of 7.48 gallons per cubic foot:
Volume in gallons = 87.16 ft^3 * 7.48 gallons/ft^3
Volume in gallons ≈ 651.3 gallons
Therefore, the water tank holds approximately 651.3 gallons.