SOLUTION: A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each end. If the overall length of the tank is 20 ft and the voulme is 50 pie cubic ft, find th

Algebra ->  Volume -> SOLUTION: A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each end. If the overall length of the tank is 20 ft and the voulme is 50 pie cubic ft, find th      Log On


   

Question 678036: A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each end. If the overall length of the tank is 20 ft and the voulme is 50 pie cubic ft, find the common radius of the hemispheres and the cylinder.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each end.
If the overall length of the tank is 20 ft and the volume is 50 pie cubic ft,
find the common radius of the hemispheres and the cylinder.
:
Let r = the common radius
The length of the cylinder portion = (20-2r)
:
hemisphere volumes + cylinder portion = 50pi
4%2F3*pi%2Ar%5E3 + pi%2Ar%5E2%2820-2r%29 = 50%2Api
divide thru by pi
4%2F3*r%5E3 + r%5E2%2820-2r%29 = 50
:
4%2F3*r%5E3 + 20r%5E2-2r%5E3%29 = 50
multiply by 3
4r%5E3+%2B+3%2820r%5E2-2r%5E3%29 = 3(50)
:
4r%5E3+%2B+60r%5E2+-+6r%5E3 = 150
:
-2r%5E3+%2B+60r%5E2+-+150 = 0
simplify, divide by -2
r%5E3+-+30r%5E2+%2B+75 = 0
:
solve it graphically
+graph%28+300%2C+200%2C+-5%2C+5%2C+-100%2C+100%2C+x%5E3-30x%5E2%2B75%29+
:
r = 1.626 ft, is the common radius