A cylindrical tin can , closed at both ends of a given volume , has to be constructed . Prove that , the amount of tin required will be least , when the height of the can is equal to its diameter .

A cylindrical tin can open at the top , of a given capacity has to be constructed . Show that the amount of the tin required will be least if the height of the can is equal to its radius

A cylindrical tin can, open at the top, of a given capacity has to be constructed, show that the amount of the tin required will be least if the height of the can is equal to its radius.

The sum of the surface of a sphere and a cube is given. Prove that the sum of their volumes is least when the diameter of the sphere is equal to the edge of the cube.

Prove that, a conical tent of given capacity will required the least amount of canvas, when the height is sqrt2 times the radius of the base.

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

A cuboidal tank is filled with diesel. That amount of diesel is poured into 240 tins in such a way that each of the tins volume is 15 lit. If the breadth of the tank is 1.5 m and the height of the tank is 3/5th times of its length, then find the height and length of the tank.

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.