Ijust purchased a swimming pool with the dimensions of 15 feet across and 42 inches deep. yes it is a circle. i need to know how many gallons of water it will hold. i am having a tanker brought out and need to know how much they need to bring because they charge by the gallon to bring it out.

When the pool is full to the rim, you'll have a cylinder of water.  The diameter
of the cylinder is 15-ft, and the height of the cylinder is 42 inches.

Here are the tools you'll need:

-- Volume of a cylinder = (pi) (radius squared) (height)
-- Radius = 1/2 diameter = 7.5 feet
-- Keep everything in the same units.  Depending on which unit
you prefer,  7.5 feet = 90 inches,  and 42 inches = 3.5 feet.

I like inches and cubic inches, because I remember that
1 gallon = exactly 231 cubic inches.

Volume of the cylinder = (pi) (radius squared) (height)

Volume = (pi) (90 squared) (42) = (pi) (8,100) (42) = 1,068,769.8 cubic inches

1,068,769.8 / 231 = 4,626.7 gallons

Slightly easier:

about 7.48 gallons = 1 cubic foot

Volume = (pi) (7.5-ft squared) (3.5-ft) = 618.5 cubic feet

(618.6 cubic-ft) x (7.48 gallons per cubic-ft) = 4,627.1 gallons

The results are not identical, but don't panic.  They are equal
to within about 51 ounces (0.009 percent).  The tanker will either
spill or evaporate more than that during the process of the delivery.

By the way ... you'd be wise not to install the pool on the second floor.
That much water weighs a little over 19.3 tons !