How to Calculate Volume and Weight of Air in an Auditorium

In summary, the problem involves finding the volume in cubic feet and weight of the air in a room, given its dimensions and density. The volume is calculated to be 339020 ft^3 using basic dimensional analysis, while the weight can be found by multiplying the density with the volume and converting to pounds. The conversation also includes a mistake made by one of the individuals and a comment about their proficiency in calculus.
  • #1
svtec
22
0
Here is the problem:

An auditorium measures 40.0m X 20.0m X 12.0m. the density of the air is 1.20kg/m^3.

a) what is the volume in cubic ft?

b) the weight of the air in the room in pounds.

for a) i have some big answer. 339020 ft^3. using V=l*w*h and then using basic dimensional analysis to convert from cubic meters to cubic ft. (my answer in metric was 9600m^3.

for b) i have no clue how to convert a density to a weight.

any pointers or suggestions would be great.

TIA...

-andrew
 
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  • #2
Multiply Density with Volume to get the weight in Kg , and do the conversion into pounds.
 
  • #3
thanks for the help.

that was a total rookie mistake that i made.

<------ is done with calculus, but cannot manipulate a simple equation.
 

FAQ: How to Calculate Volume and Weight of Air in an Auditorium

What is volume and density?

Volume is the amount of space occupied by a substance or an object. It is usually measured in cubic units such as centimeters or liters. Density, on the other hand, is the measure of how much mass is contained in a given volume. It is expressed in units of mass per unit of volume, such as grams per cubic centimeter.

How do you calculate volume and density?

Volume can be calculated by multiplying the length, width, and height of an object or by using the appropriate formula for the shape of the object. Density is calculated by dividing the mass of an object by its volume. The formula for density is mass divided by volume (D=m/v).

What are some common units of measurement for volume and density?

Some common units of measurement for volume are cubic centimeters, liters, and cubic meters. Common units of measurement for density include grams per cubic centimeter, kilograms per cubic meter, and pounds per cubic inch.

How does temperature affect volume and density?

Temperature can affect volume and density because as temperature increases, the volume of a substance usually increases as well. This is due to the increased motion of particles at higher temperatures. However, the density of a substance may decrease with increasing temperature if the substance expands more than its mass increases.

How are volume and density related to each other?

Volume and density are directly related to each other. As the volume of a substance increases, its density decreases, and vice versa. This means that if the volume of a substance decreases, its density will increase if the mass remains the same. This relationship is described by the formula density = mass/volume (D=m/v).

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