SOLUTION: Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubi

Algebra ->  Radicals -> SOLUTION: Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubi      Log On


   

Question 265854: Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubic inches. What should the radius of the cylinder be?
The name of the lesson is Fundamental Theorem of Algebra.
Do i need to find the roots to get the radius?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubic inches. What should the radius of the cylinder be?
:
Let r = the radius of the cylinder (and the hemisphere)
then
(r+3) = the height of the cylinder
:
vol of a sphere =%284%2F3%29pi%2Ar%5E3, therefore
vol of a hemisphere = %282%2F3%29pi%2Ar%5E3
:
vol of cylinder + vol of hemisphere = 72*pi
pi%2Ar%5E2%2Ah + %282%2F3%29pi%2Ar%5E3 = 72pi
:
Divide thru by pi and eliminate that
r%5E2%2Ah + %282%2F3%29%28r%5E3%29 = 72
:
Replace h with (r+3)
r%5E2%2A%28r%2B3%29 + %282%2F3%29r%5E3 = 72
:
r%5E3%2B3r%5E2%29 + %282%2F3%29r%5E3 = 72
:
Add like terms r^3 + 2/3*r^3
%285%2F3%29%28r%5E3%29 + 3r%5E2 = 72
:
Multiply each term by 3
5r%5E3+%2B+9r%5E2 = 216
:
5r%5E3+%2B+9r%5E2+-+216 = 0
:
Graph this equation, find x intercept
+graph%28+300%2C+200%2C+-4%2C+10%2C+-100%2C+300%2C+5x%5E3%2B9x%5E2-216%29+
r = 3 inches the radius
:
Check; find the volumes
pi%2A3%5E2%2A6 = 169.646
%282%2F3%29pi%2A3%5E3 = 56.487
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Total volume is 226.195 divide this by pi you have 71.999 ~ 72