Welcome to our lesson on calculating density as a compound measure of mass and volume. So to work out a density we're going to use this formula here where density is mass divided by volume. So in question one we're asked to calculate the density of a piece of metal where the mass is 12 grams and the volume is 6 centimeters cubed.
So we'll use our formula where the density is equal to the mass, which is 12 grams, divided by the volume, which is 6 centimeters cubed. So the density is 12 divided by 6, which is 2, and grams divided by centimeters cubed are our units. So the density of a piece of metal is 2 grams per centimeter cubed. And in question b, calculate the density of a model that has a volume of 120 centimeters cubed and weighs 40 grams. So again we're going to use our formula where the density is equal to the mass which is 40 grams divided by the volume which is 120 centimeters cubed 40 divided by 120 is one third or 0.3 recurring and then grams divided by centimeters cubed are our units okay let's try some more questions so do you want to try and work out the density of this cube using a formula the mass divided by the You can pause the video and resume it when you're ready.
So to begin with we need to work out the volume of the cuboid. We can do this by working out the area of this face which is the six centimeters here multiplied by the height which is four centimeters. So the area of the face is 24 centimeters squared.
To work out the volume we multiply it by the depth. which is 3 centimeters. So the volume of a cuboid is 72 centimeters cubed and we can use this to work out the density because we have a mass of 0.15 which I'm going to convert into grams as 150 grams.
I'm multiplying this by 1000 so 150 grams is a mass. divided by the volume of 72 centimeters cubed and this is approximately 2.1 grams per centimeters cubed okay let's try one final question so in this question the density of a cuboid is 2.25 grams per centimeter cubed and we're asked to calculate the mass of a cuboid do you want to try and do this yourself by pausing the video and you can resume it when you're ready. So again we're going to need to work out the volume. So the volume will be the area of the cross section which could be this face which is 10 multiplied by the height of 12 which is 120 centimeters squared multiplied by the depth of 3 centimeters. So the volume is 360 centimeters cubed.
So we have the density as 2.25 grams per centimeters cubed. And this is the mass which we're trying to find divided by the volume of 360 centimeters cubed. So we'll multiply both sides by 360. These will cancel so we have 2.25 multiplied by 360 will be the mass which is 810 grams. Okay thank you for watching and I hope you found that useful. Thanks again and take care.