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Plutonium88
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Homework Statement
a cylinder can be inscribed upright in a circular cone with radius 4 and height 7. What is the maximum volume of a cylinder that can be inscribed inside of the cone.
Homework Equations
Image of the problem
http://s17.postimage.org/67akeibxb/Cylinder.png
The Attempt at a Solution
let rc = radius of the cone Let rt=radius of cylinder
Let hc=height of cone let ht= height of cyldiner
ht/hc = (4-rt)/rc
ht/7=(4-rt)/4
ht=7-7/4(rt)
D: 0<r<4
Vt=Volume of cylinder
Vt=Pi(rt)^2(ht)
vt=pi(rt)^2(7-7/4(rt))
vt=7pi(rt)^2 - 7/4(pi)(rt)^3
vt'=14pi(rt) - 21/4(pi)(rt)^2
vt'=0
0 =14pi(rt) - 21/4(pi)(rt)^2
0=7pi(rt)[2-3/4rt]
r=0, not true
0 = 2-3/4rt
-2 = -3/4rt
rt=8/3=2.67v'(2.5)= + numbrer
v'(2.7)= - number
therefore there is a maximum value
there fore rt=2.67 is the value which will achieve maximum volume.
h=7-7/4rt
h=2.33
vt=Pi(rt)^2h
vt=52.18m^3
Therefore maximum volume of a cylinder that can be inscribed in a cone is 52.18 m^2Okay i think i have this correct, I'm just worried i messed up my numbers and i was wondering if some one could help me out.. I've doouble and triple checked it myself... Also can anyone tell me if I'm missing any information that would be valuable?>
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