The base of a cuboid is square and its volume is given. Show that its total surface will be minimum, if it is a cube.

Show that the total surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

Show that the total surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

Show that the total surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

A given quantity of metal is to be cast into a half cylinder with a rectangular base and semicircular ends. Show that in order for the total surface area to be minimum, the ratio of the length of the cylinder to the diameter of its semi-circular ends is pi:(pi+2) .

Show that the surface area of the closed cuboid with square base and given volume is minimum when it is a cube.

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

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

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

Show that the right circular cylinder, open at the top, and of given surface area and maximum volume is such that its height is equal to the radius of the base.