# Optimization Problems

#### Draggu

1. Homework Statement
Find the dimensions of the right circular cone of maximum volume that can be inscribed in a sphere of radius 15cm.

2. Homework Equations

3. 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.

Final dimensions; r=11.5 roughly

h=24.63

maax volume is 3411.05 ?

Last edited:
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#### Draggu

Can somebody confirm this? Thank you :)

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