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.
You're falling, falling, falling... and then you wake up. This is a very common dream and is said to symbolize insecurities and anxiety. Something in your life is essentially out of control and there is nothing you can do to stop it. Another interpretation is that you have a sense of failure about something.