Show that a conical tent of given capacity will require the least amount of canvas when the height is `sqrt(2)` times the radius of its base.

Show that a conical tent of given capacity will require the least amount of canvas when the height is sqrt2 times the radius of its base.

Show that a closed cylinder of a given volume will have its least surface when its height is equal to its diameter.

For a particle projected slantwise from the ground, the magnitude of its position vector with respect to the point of projection, when it is at the highest point of the path is found to be sqrt(2) times the maximum height reached by it. Show that the angle of projection is tan^(-1) (2) .

An open tank is to be constructed with a square base and vertical sides to hold a given capacity of water . The expense of lining the tank with lead is least when the ratio of the depth and the width is

A closed clylinder of given volume will have least surface when height (h) and radius (r) are related as

Show that the semi-vertical angle of right circular cone of the maximum volume and of given slant height is tan^(-1) sqrt(2)

The radius of a conical tent is 7 metres and its height is 10 metres. Calculate the length of canvas used in making the tent if width of canvas is 2m. [" Use "pi=22/7]