What is the formula for determining the volume of water in a cistern?

Question

tank sized 8 feet in diameter by 10 in depth. How much water will it hold?

Answer 1

Volume of a cylinder is pi * r^2 * height.

Radius is half of diameter, so for an eight-foot diameter, the radius is four feet.

Also, I assume that you mean "10 [feet] in depth" and not "10 in[ches] depth."

v = pi * r^2 * h
v = pi * (4ft)^2 * (10ft)
v = 502.655 ft^3

... which rounds off to 503 cubic feet.

One cubic foot is 7.481 gallons of water, so the answer in gallons is 502.655*7.481 =~ 3,760.4

Answer 2

First, make sure the units for diameter and depth are the same - for example, convert the depth from 10 inches to feet ...
1 in = 1/12 foot = .08333 ft.
So, 10 in = 10(.08333) ft = .8333 ft.
Now, Volume = Area X Depth = pi (Dia^2)/4 ft^2 X .8333 ft
= 41.9 ft^3.

To convert this to cubic inches (in^3), multiply by 1,728 in^3/ft^3, which gives 7.24 x 10^4 in^3.