Hemisphere is the exact half of a sphere. When a plane cuts across a sphere at its center, it forms two hemispheres. Surface area of a hemisphere of radius r is given by 2pr2. Volume of a hemisphere of radius r is given by 2/3pr3.
Falling dreams also often reflect a sense of failure or inferiority in some circumstance or situation. It may be the fear of failing in your job/school, loss of status, or failure in love. You feel shameful and a lost sense of self-esteem You are unable to keep up with the status quo and feel that you don't measure up.
If you were trying (or straining) to reach a high altitude, the dream is telling you that your grasp is greater than your reach, and you would be wise to alter your course. When I dream about flying, I can soar as high in the air as I desire and then swoop down toward the ground.