Question

A lecture hall measures 40.0m X 20.0m. The density of air is. 1.20km3. What (a) the volume of the room in cubic feet and (b) the weight of air in the room in pounds?

Answer 1

The volume of the room is 68,556.8 cubic feet and the weight of air in the room is 5,259.99 pounds.

Step-by-step explanation:

To find the volume of the room in cubic feet, we need to convert the dimensions from meters to feet. Since 1 meter is approximately equal to 3.28 feet, the length of the room is 40.0 m x 3.28 ft/m = 131.2 ft and the width of the room is 20.0 m x 3.28 ft/m = 65.6 ft.

To find the volume in cubic feet, we multiply the length, width, and height of the room. Assuming a standard height of 8.0 feet, the volume would be 131.2 ft x 65.6 ft x 8.0 ft = 68,556.8 cubic feet.

To find the weight of air in the room in pounds, we need to know the density of air. The density of air is given in the question as 1.20 kg/m^3. We can convert this to pounds per cubic foot by using the conversion factor 1 kg = 2.20462 pounds and
`1 m^3 = 35.3147 cubic feet.` The density of air in pounds per cubic foot is then
`1.20 kg/m^3 x 2.20462 pounds/kg x (1 m^3 / 35.3147 ft^3) = 0.07673 pounds/ft^3.`

To find the weight of air in the room, we multiply the volume of the room by the density of air. The weight of air in the room is

`68,556.8 cubic feet x 0.07673 pounds/ft^3 = 5,259.99 pounds.`