If there are 7.5 gallons to the cubic foot, and a spherical storage tank has a radius of 19.5 ft, then using 3.14159 for p ,how many gallons, correct to the nearest whole gallon, will the full storage tank hold?
Please show your work. Calculate the volume of the sphere in cubic feet and convert it to gallons. You should know the sphere volume formula.
Whoever assigned this problem gave you an inaccurate conversion factor. There are 7.48051945 gallons per cubic foot. If you use 7.5, you will be off by more than a gallon in your answer.
It is ridiculous to use six significant figures for pi when the conversion factor is only accurate to two figures.
You may quote me.
To find the volume of a spherical storage tank, we can use the formula:
V = (4/3) * π * r^3
Where:
V represents the volume of the tank,
π represents the mathematical constant pi (approximately 3.14159),
r is the radius of the tank.
Given that the radius of the tank is 19.5 ft, we can substitute this value into the formula:
V = (4/3) * 3.14159 * (19.5)^3
Now, we can calculate the volume:
V = (4/3) * 3.14159 * 19.5^3
V = (4/3) * 3.14159 * 7414.175
V ≈ 91934.803 ft^3
Since there are 7.5 gallons in one cubic foot, we can calculate the number of gallons in the tank:
Gallons = 91934.803 ft^3 * 7.5 gallons/ft^3
Gallons ≈ 689512.5275 gallons
Rounded to the nearest whole gallon, the full storage tank will hold approximately 689,513 gallons.