how many square ft. of floor space does a house have if it has 96 inch
high celing and 32,000 ft3 volume?
The answer as stated is 4000 ft2 or 4000 square feet. To be able to figure these out, you need to know the formula for figuring volume for a box.
Length (feet) x Width (feet) x Height (feet) = Volume (ft3 or cubic feet)
Length and width are unknown, so we'll use x and y for those.
Height is given in inches, you must convert this to feet to have a workable equation.
96 in/12in/foot = 8 feet. Never drop your units (feet, inches, ohms, whatever).
x ft times y ft times 8 feet = 32,000 ft3 or
(x')(y')(8ft) = 32,000ft3
rearrange to solve for x and y (length and width)
x' times y' = 32,000ft3/8ft
x' times y' = 4000ft2, final answer
x' times y' is your area, which is measured in square feet. Without knowing one of those numbers, you cannot know the dimensions of the building (could be 40' x 100', 50' x 80', etc.)