The description for a certain brand of house paint claims a coverage of 460ft^2/gal.
A) Express this quantity in square meters per liter.
B)Express this quantity in quantity in a SI unit (i.e, meters to the power-1, looks like m-1)
C)What is the inverse of the original quantity?
A) Multiply 460 ft^2/gal by the conversion factors
(0.3048 m/ft)^2 and (1 gal/3.785 l)
B) 1 m^2/l = 1 m^2/10^-3 m^3 = 10^3 m^-1
Multiply your result from A) by that conversion factor
C)Take the recirocal of the answer in B). The units will be m^3 required per m^2 of coverage. It will be equivalent to the thickness of one coat of paint.
A) To convert square feet (ft^2) to square meters (m^2), you need to use the conversion factor of 0.0929 m^2/ft^2.
To get the coverage in square meters per liter, first convert gallons to liters. Since 1 gallon is approximately equal to 3.785 liters, divide 460 ft^2 by 3.785 liters:
460 ft^2/ (3.785 liters) = 121.57 ft^2/liter
Now, multiply this value by the conversion factor:
121.57 ft^2/liter * 0.0929 m^2/ft^2 = 11.30 m^2/liter
So, the coverage in square meters per liter is approximately 11.30 m^2/liter.
B) To express the quantity in an SI unit as meters to the power -1, we can use the reciprocal of the square meters per liter.
Reciprocal of 11.30 m^2/liter is 1/(11.30 m^2/liter) = 0.0885 liters/m^2
Therefore, the quantity can be expressed as 0.0885 liters/m^2.
C) The inverse of the original quantity is the reciprocal. In this case, the original quantity is 11.30 m^2/liter.
The inverse or reciprocal of 11.30 m^2/liter is 1/(11.30 m^2/liter) = 0.0885 liters/m^2.
So, the inverse of the original quantity is 0.0885 liters/m^2.