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.
A man that is slowly falling out of his bed as he is fast asleep, might have a dream that he is falling from a sky scraper. His subconscious mind is interpreting the physical action of falling from his bed, and converting it to the dream language of falling from a skyscraper.