I have a well and only basic math skills.
I need to find out how much water in gallons can be held in a well casing of 24 inches diameter and a depth of 15 feet.
Can any of you math geniuses help me out?
Thanks!
well that is a cylinder.
Assuming your well is a cylinder you have 47.1 cubic feet of water. This is about 352 gallons.
352 U.S. liquid gallons, which is about 293 Imperial gallons.
Convert to metric, do it quickly in your head, convert back again. That’s why metric was invented. One liter of water weighs one kilogram and occupies 1,000 cubic centimeters…
Convert your linear measurements to metric (2.54 cm/in)
24 in X 2.54cm/in = 60.96cm diameter (30.48cm radius)
15 ft X 12 in/ft X 2.54 cm/in = 457.2cm depth
Volume of a cylinder is equal to depth times area of the cross section.
Area of a circle = pi X the square of the radius, so (10.78cm)[sup]2[/sup] X pi = 929.0304cm[sup]2[/sup] X 3.14159 = 2919cm[sup]2[/sup]
2919cm[sup]2[/sup] X 457.2cm = 1334400cm[sup]3[/sup]
That’s how many cc of water fits when the well is full to the brim. To convert to liters, divide by 1000 for 1334.4 liters
There are 1.056 quarts in a liter, so multiply by 1.056 to get the number of quarts 1334.4 X 1.056 = 1408 quarts (roughly. I’m fudging the numbers to achieve an even number of gallons).
There are four quarts in a gallon, so divide that by four to get the number of gallons 1408/4 = 352 gallons.
Or, you could just stay in imperial measurements and use the fact that there are 231 cubic inches in a gallon of water (standard temperature and pressure).
15 feet = 180 inches => 180 x 12[sup]2[/sup] X pi / 231 = 352 gallons
Nitpick: there are 231 cubic inches in a gallon of water using U.S. customary measurements, not imperial!