Question

The density of a certain type of paint is 1.2 grams per cubic centimeter. A garage Door that is 3 meterá tal and 7 meters wide is to be painted with a 1-millimeter-thick coat of paint (on the outside only.)

What is the mass(in grams) of the paint that will be needed to paint the door?

Answer 1

Since the density is given in grams per cubic centimeter, we are going to convert the dimensions of the door to centimeters to calculate its volume in cubic centimeters.
We know that 1 meter = 100 centimeters and 1 centimeter = 10 millimeter, so we can use those conversion factors to convert from millimeters to centimeters and from meters to centimeters:

`3m( (100cm)/(1m) )=300cm`

`7m( (100cm)/(1m) )=700cm`

`1mm( (1cm)/(10mm) )=0.1cm`
The volume of the layer of the paint will be height times wide time thickness, so:

`V=(300cm)(700cm)(0.1cm)`

`V=21000cm^3`

Now, to find the mass needed to paint the door, we are going to use the formula:
`M=DV`
where

`M` is mass

`D` is density

`V` is volume
We know from our problem that
`D= (1.2g)/(cm^3)`, and we know form our previous calculation that
`V=21000cm^3`, so lets replace those values in our formula to find
`M`:

`M=DV`

`M=((1.2g)/(cm^3) )(21000cm^3)`

`M=25200g`

We can conclude that we will need 25200 grams of paint to paint the door.