Final answer:
To calculate how many gallons of water a spherical tank with a diameter of 25 feet can hold, we find the volume of the tank in cubic feet and then convert that to gallons using the conversion factor of approximately 7.48 gallons per cubic foot, resulting in the tank holding approximately 61097.44 gallons of water.
Step-by-step explanation:
The question involves finding the volume of water a spherical tank can hold. The diameter of the spherical water tank is given as 25 feet.
To find the volume, we use the formula for the volume of a sphere which is V = (4/3)πr3, where r is the radius of the sphere.
Since diameter is twice the radius, r = diameter / 2 = 25 feet / 2 = 12.5 feet.
To convert the cubic feet to gallons, we use the conversion factor that there are approximately 7.48 gallons of water in 1 cubic foot.
First, calculate the volume of the sphere:
- V = (4/3)π * (12.5 feet)3
- V ≈ (4/3)π * 1953.125 cubic feet
- V ≈ 4.18879 * 1953.125 cubic feet
- V ≈ 8168 cubic feet approximately
Then, convert the volume to gallons:
- Total gallons = Volume in cubic feet * Gallons per cubic foot
- Total gallons = 8168 cubic feet * 7.48 gallons/cubic foot
- Total gallons ≈ 61097.44 gallons
The spherical water tank will hold approximately 61097.44 gallons of water.