Question Video: Calculating the Mass of Fluid Displaced by a Rectangular Prism

The rectangular-prism-shaped solid object shown in the diagram is submerged in water with a density of 1000 kg/m³. What mass of water is displaced by the object when it is fully submerged?

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Video Transcript

The rectangular-prism-shaped solid object shown in the diagram is submerged in water with a density of 1000 kilograms per meter cubed. What mass of water is displaced by the object when it is fully submerged?

Okay, so in this question, we’ve got this solid object that we’ve submerged in water. And we know that water has a density of 1000 kilograms per meter cubed. What we’ve been asked to do is to find out what mass of water is displaced by the object when the object is fully submerged. In other words, the object is fully under water. What this means is that the volume of water that is displaced is the same as the volume of the solid object. So let’s work out the volume of the solid object.

We can recall that the volume of a rectangular-prism-shaped object or a cuboid is given by multiplying the width of the cuboid by the length of the cuboid by the height of the cuboid. And in this case, 3.5 meters is its width, 2.5 meters is its length, and 2.5 meters is its height. So the three quantities we’ve been given in the diagram need to be multiplied together to find the volume of the solid object. And hence, we say that the volume is equal to 3.5 meters times 2.5 meters times 2.5 meters. And when we evaluate this, we find that it is equal to 21.875 meters cubed.

Now, remember the volume of water that we displace is the same as the volume of the solid object. Therefore, this is also the volume of water that is displaced. So why is this useful? Well, we can recall that the mass of any object is given by multiplying the density of that object 𝜌 by the volume that it occupies 𝑉. And since we’re trying to find out the mass of the water, to find out this mass, we need to multiply the density of the water by the volume of the water.

And once again, the volume of the water is the volume that the water would have occupied if the block — the solid object — wasn’t there because we’re trying to work out the mass of the displaced water. So anyway, we say that the mass of the displaced water is equal to the density 1000 kilograms per meter cubed multiplied by the volume 21.875 meters cubed.

And because we’re using standard units here for both of the quantities, density is given in kilograms per meter cubed and volume is given in meters cubed. Our final answer for the mass is also going to be in its standard unit, which is the kilogram. So when we evaluate the numerical value on the right-hand side, we’ll know that that’s the mass in kilograms.

And when we do evaluate it, it ends up being 21875 kilograms. And this is our final answer.

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