Need help approaching a quadratic, simultaneous equation
It's been overs ten years since my last calculus course, and I think I've regressed back to a pre-algebra level. Not looking for an answer here, just help getting started.
What I think I have here is a simultaneous equation, but I'm not sure... as I try to work it out, I keep getting stuck with what seems like a quadratic equation. I'm sure I'm wrong on one or both counts, so can someone lend some perspective?
I'm trying to design a cylinder with dimensions proportional to a larger cylinder.
The diameter of the original cylinder = 26.24 ft
The height of the original cylinder = 12.08 ft
This gives a diameter to height ratio of 2.172.
I'd like to find the dimensions necessary to design a 0.668 cubic foot cylinder while maintaining the proportions of the larger cylinder, so I've come up with the following simultaneous equations:
diameter = X (in feet)
height = Y (in feet)
(X/2)2 * PI * Y = 0.668 cubic feet
X/Y = 2.172
I've tried to solve for X in the first equation...
X2/4 * PI * Y = 0.668
X2 * PI * 4Y = 4 * 0.668 = 2.672
X2 * 4Y = 2.672 / PI
X2 = 0.2126 / 4Y
X2 = 0.05316 / Y
X = SQRT (0.05316 / Y)
... and then insert it into the second equation...
(SQRT (0.05316 / Y)) / Y = 2.172
(SQRT (0.05316 / Y)) = 2.172Y
(SQRT (0.05316 / Y))2 = 4.7176Y2
0.05316 = 4.7176Y2 / Y
0.05316 = 4.7176Y
Y = 0.0113 feet
This would make the height of the cylinder 0.135 inches, and the diameter 0.35 inches. This isn't right.
I'm sure this is simple and that I'm making it overly complex. Still, any help would be really appreciated. Thanks!
Re: Need help approaching a simultaneous equation
One error is in this line:
X2 = 0.2126 / 4Y
If you try 2.672/pi you get an answer of 0.850524 and not 0.2126.
Try using this value instead and see how you go.