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Draggu
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Homework Statement
Find the dimensions of the right circular cone of maximum volume that can be inscribed in a sphere of radius 15cm.
Homework Equations
The Attempt at a Solution
let r be radius of circular base of cone
let y be height of small right triangle
let h be height of cone
r^2 + y^2=225
y=sqrt(225-r^2)
h=15+y
V=(1/3)pir^2(sqrt(225-r^2) + 15)
Now to find V'...I get to 9r^4-2670r^2+195750 = 0
0=3(3r^4-890r^2+65250)
Need to solve for r.
Took about 2323 lines.
Final dimensions; r=11.5 roughly
h=24.63
maax volume is 3411.05 ?
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