Find the maximum volume of the cylinder

[danago]

A cylinder is placed into a right cone which has a radius of 1m and a height of 2m. Find the maximum volume of the cylinder.

I think i am able to do it, but I am not 100% sure if I am correct. I first used similar triangles to write the radius of the cone at any height from its apex. i came up with h=2r.

Now, if i let the radius of the cylinder be R, then the height that it rests at is 2R. Since the cone is 2m high, the height of the cylinder will be 2-2R.

The volume is given by $$V = \pi R^2 (2 - 2R)$$, which i used calculus to maximize and came up with R=2/3, therefore V=~0.93. Does that look right?

Thanks in advance,
Dan.

 

[Dick]

Looks fine. Kind of a confusing double use of 'height' though. I'd use another word for the apex distance if I were describing it.

 

[danago]

Alright thanks for confirming that