If we wind half of the surface of sphere with cord as shown in the figure, and then wind with exactly the same length of the cord the surface of a cylinder having just the same radius, the height of the cylinder equaling the diameter, we find that the cord covers half of the curved surface of the cylinder.

            Therefore, the surface area of a sphere equals the curved surface area of a cylinder of the same radius and height.

            Here the height of the cylinder,  being the radius of the sphere and also the radius of the circular base of the cylinder.
                    Area of the curved surface of the cylinder
                        Hence, the surface of a sphere,
Note, that the surface of a sphere is equal to the area of four of its great circles.

Summary:

1. Area of the surface of a sphere  or  sq.units, whereis the radius andis the diameter.
2. Total surface area of the hemi-sphere  sq.units

Example:
            A solid is composed of a cylinder with hemisphere ends. If the whole length of the solid is 108cm and diameter of the hemi-spherical ends is 36cm, find the cost of polishing the surface at the rate of $7 per sq.cm.
Solution:

Example:
            A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is 6cm and its height is 4cm. Calculate the surface area of the toy.
Solution: