What must be the height of the lamp for maximum illuminance at the edge?

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is 20/sqrt3 cm. Also find the maximum volume of the cylinder.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 20 cm is 40/sqrt3 cm. Also find the maximum volume of the cylinder.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 30 cm is 60/sqrt3 cm. Also find the maximum volume of the cylinder.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R/sqrt3 . Also find the maximum volume.

What must be the shape of a gaussian surface?

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

At what temperature, the density of water is maximum?

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the orginial cylinder