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.
The dream of falling and the sensation of falling while sleeping stems from regaining lucidity when you are floating outside the body. Our brain normally tries to incorporate external sensations and stimuli into our dreams, especially when we are in the REM period close to the time when we wake up every day.