Houdini's Escape

[schf0ol3d]

I am not the one to go around for calculus help, but this one problem has had my partner and I stumped for quite some while.

Houdini's Escape (Click here for problem)

I honestly need help by even approacting this problem. My partner and I thought of using an intergral of Pi(r(z))^2 from 1 to 7+h, where h is the height of the block, but our teacher brought us to the conclusion that that approach wasn't the correct one.

Any help is greatly appreciated. Thank you!

 

[galactus]

You could find the equation of the side of the flask by using the appropriate line equation which represents it.

It passes through (10,1) and (10/sqrt(7),7)

It's equation in terms of x is:

\(\displaystyle \L\\x=\frac{5\sqrt{7}y}{21}-\frac{5y}{3}-\frac{5\sqrt{7}}{21}+\frac{35}{3}\)

Now, use:

\(\displaystyle \L\\{\pi}\int_{1}^{h}x^{2}dy\)

This should give you the volume with respect to height.

Another Houdini problem was posted about a week ago. Search it out and look it over. It may help.