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

Show that a cylinder of given volume, open at the top, has minimum total surface area if its height is equal to radius of the base.

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.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 time the radius of the base.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.

Show that the height of a closed right-circular cylinder of given volume and least surface area is equal to its diameter.

If the height of a cylinder is doubled and radius remains the same, then volume will be

Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm^2 .

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.