Home
Class 12
MATHS
A right circular cylinder of maximum vol...

A right circular cylinder of maximum volume is inscribed in a given right circular cone of height `h` and base radius `r`, then radius of cylinder is:

Text Solution

Verified by Experts

As `/_AFE and /_ACG` are similar triangles
so, `/_AEF=/_ACG` `(h1)/x=h/r`
`h1=hx/r`
Volume of cylinder=`pix^2(h-h1)=pihx^2(1-x/r)` For maximum volume,
`(dv)/dx=0`
`pih(2x-3x^2/r)=0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that the height of the circular cylinder of maximum volume that can be inscribed in a given right-circular cone of height h is 1/3 h

Show that the height of the right circular cylinder of maximum volume that can be inscribed in a given right circular cone of height h is (h)/(3)

Find the altitude of a right circular cylinder of maximum volume inscribed in a sphere of radius r.

The height of a right circular cylinder of maxium volume inscirbed in a sphere of radius 3 is

The height of a right circular cylinder of maxium volume inscirbed in a sphere of radius 3 is

The radius of cylinder of maximum volumne which can be inscribed in a right circular cone of radius R and height H ( axis of cylinder and cone are same ) H given by

The radius of cylinder of maximum volumne which can be inscribed in a right circular cone of radius R and height H ( axis of cylinder and cone are same ) is given by

Find the height of a-right circular cylinder of maximum volume, which can be inscribed in a sphere of radius 10 cm.