Posted by **sara** on Sunday, December 25, 2011 at 1:08am.

Calculate the height of a cylinder of maximum volume that can be cut from a cone of height 20 cm and base radius 80 cm ,

please help me

- Calculus -
**Damon**, Sunday, December 25, 2011 at 3:01am
radius = r = 80 - (80/20)h

r = 80 - 4 h

v = pi r^2 h

v = pi (80-4h)^2 h

dv/dh = 0 for max or min

0 = (80-4h)^2 + h (2)(80-4h)(-4)

0 = 6400-640h+16h^2 - 640h+32h^2

48h^2 - 1280 h + 6400 = 0

6 h^2 - 160 h + 800 = 0

3 h^2 - 80 h+ 400 = 0

(3 h - 20 )(h - 20 ) = 0

h = 30 (no good, minimum)

or

h = 20/3 approximately 7

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