cylinder in a cone problem

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kpx001

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this is the cylinder constructed inside a cone with a base radius R=10 and height of 30. how would i find the formula for this cone in order to find the r (not R which is the cone radius)that gives the largest possible volume ? i tried (1/3) * pi * radius2 * height - pi*r^2*h with the change but im completly lost cuz i got a huge number.

 
Please show us your work , even if you think it is wrong - so that we know where to begin to help you.
 
(1/3) * pi * 10^2 * 30 - pi*r^2*(30-H) ?
i know i have to take the derivative but unsure if my function is correct
 
kpx001 said:
(1/3) * pi * 10^2 * 30 - pi*r^2*(30-H) ?
i know i have to take the derivative but unsure if my function is correct
Click to expand...

Whose volume you are trying to find - or trying to maximize?
 
i need to find the cylinders radius that gives the largest possible volume
 
I am moving this to calculus since it is more of a calc problem.

Let R and H be the radius and height of the cone, and r and h be the radius and height of the cylinder.

The volume of the cylinder is \(\displaystyle V={\pi}r^{2}h\)

Now, as in a lot of these problems, use similar triangles.

\(\displaystyle \frac{H-h}{H}=\frac{r}{R}\)

Therefore, \(\displaystyle h=\frac{H}{R}(R-r)\)

Plug this into the cylinder volume equation at the top. H and R are given constants.

Then differentiate to find dV/dr. Set to 0 and solve for r.

If done correctly, you should find that the volume of the cylinder that has max volume is 4/9 the volume of the cone.
 

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galactus said:
If done correctly, you should find that the volume of the cylinder that has max volume is 4/9 the volume of the cone.
Click to expand...
Important to know if the cylinder is to be filled with Smirnoff's :idea:
 
kpx001 said:
i need to find the cylinders radius that gives the largest possible volume - of what?

you have three things - (1) the original cone (2) the cut-out cylinder and (3) the part of cone from which cylinder was cut-off

which volume do you want to maximize?
Click to expand...
 
I am pretty sure they are asking for the classic maximum volume of the cylinder inscribed in a cone of known radius and height.

Try the max volume of a cone inscribed in a sphere of radius R. I don't think it matters much anyway as the poster has not returned to confirm, deny, or say thanks.
 
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