An object that floats displaces 12 kilograms of water. The water has a density of 1000 kilograms per meter cubed. How many cubic meters of water does the object displace?
Okay, so in this question, we’ve got some water and we have some random object floating in the water. Now, in order for this object to be floating in the water, it has to have displaced some water because the object is occupying some volume that was initially occupied by some water. And this is the water that got displaced.
Now what we’ve been asked to do is to work out the volume of the water that got displaced. And we need to do this having been given the mass of the water that was displaced and the density of the water. So we can recall that the density of an object 𝜌 is defined as the mass per unit volume — in other words how much mass there is packed into every one meter cubed — the mass divided by the volume.
And since in this case we’re trying to find out what the volume is, we need to rearrange this equation. We do this by multiplying both sides of the equation by 𝑉 divided by 𝜌. This way on the left-hand side the 𝜌s cancel and on the right-hand side the 𝑉s cancel. Well, that leaves us with is that 𝑉 is equal to 𝑚 divided by 𝜌. In other words, the volume is equal to the mass divided by the density.
At which point, we can plug in the values that we’ve been given in the question. The mass is 12 kilograms and the density is 1000 kilograms per meter cubed. So the volume is going to be 0.012 meters cubed And this is the volume of the water that is displaced.
In other words, 0.012 cubic meters of water are displaced by the object.