Do I need to convert gallons into cubic feet if using the data in a volume equation?

Question

School starts tomorrow, and this one problems has been driving me crazy all summer.

Some cylindrical pool has 2292 gallons of water, 5 feet in depth, and I need to find the radius. But to use the formula (V=pi*r^2*h), I need the volume, and gallons don't work with feet, right? I Googled how to convert gallons to cubic feet, and i got 306.395 ft^3. I should be using that data, right?

I've never had to convert gallons to cubic feet, and nowhere in the packet does it show you how. Am I thinking to much about this, or were my instincts correct?

Answer 1

Your instincts were correct to convert from gallons to cu.ft. The geometry aspect of the problem is now solved and what is left is an algebra problem where you must solve for the unknown.

V = pi*r^2*h = 306.396 cu.ft.
pi = 3.141592
h = 5 ft.

306.396 = (3.141592*r^2)*5
306.396 / 5 = 3.141592*r^2
61.279 / 3.141592 = r^2
19.506 = r^2
sqrt 19.506 = r
4.417 ft. = r

Check your work by plugging in the 'r' to the original formula and solve for 'V'.

V = pi*r^2*h
V = 3.141592*4.417^2*5 = 306.460 (which is close enough due to the rounding of obtained values.

Answer 2

Your instincts were correct. You must be careful with units. Convert the gallons to cu ft. Now the h in the formula is the 5 ft depth and you solve for r - which I presume you can do

It is a very positive sign that you have been mulling over the unit conversion issue - as you proceed in math and physical science you will run into unit issues over and over.

Answer 3

You need to convert gallons into cubic feet because the height and radius of the pool are measured in feet.

32,600 gallons equals 4,356 cubic feet that's 0.1336 ft^3/gal

0.1336ft^3/gal*2292gal=306.2112 ft^3 so it's going to be a little over 306 and the exact decimals depend on who you go to as a source for the calculation and where they do the rounding up or down.

call it 306.3 (roughly halfway between 306.395 and 306.211)
306.3=pi*r^2*5
r^2=306.3/(5pi)
r^2=306.3/(5*3.1416)
r^2=306.3/15.7
r^2=19.5
r=4.4 feet

Answer 4

If I am understanding you correctly, you are looking for the number of cubic feet (total volume) that are required to contain 2292 gallons of water. If so, then lets try this.

One gallon = 231 cubic inches, and
One cubic foot = 1728 cubic inches, so
2292 gallons x 231 cubic inches =
529,452 cubic inches (total volume)

Now 529,452 (total volume) / 1728 (one cubic foot) = 306.396 cubic feet.

Answer 5

You need to convert. The conversion will give you the volume; you have the depth, so the unknown is the radius. You've analyzed it coorectly.

Answer 6

Yes.
1 (cubic foot) = 7.48 US gallons

2292 gallons X 1 cubic foot/7.48 gallons = 306 cubic feet

Then just plug and solve for "R"