Video: Finding the Volume of a Cuboid in a Real-World Context

Olympic gold medal winter Ian Thorp competes in a pool with required dimensions 25 by 50 by 2 meters. What is the volume of the Olympic-sized pool?

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Video Transcript

Olympic gold medal winter Ian Thorp competes in a pool with required dimensions 25 by 50 by two meters. What is the volume of the Olympic-sized pool?

The first thing we would want to do is make a sketch of what the pool might look like. In this case, our pool has a width of 25 meters. So we can label this side 25 meters. The length of the pool would be 50 meters, and the depth of the pool is two meters. Now that we have a visual of this pool, we need to remember what volume is.

The volume of any solid is equal to the area of the base times the height. What is the base of this pool, and how would we find the area of that base? We could think of the base of this pool as the bottom of the pool, the area of the flat surface that makes up the bottom of the pool. And the bottom of this pool is a rectangle. So to find the area of a rectangle, we multiply the length times the width.

To start finding the volume here, we’ll need to multiply the length times the width of this base rectangle of our pool. The pool has a length of 50 meters and a width of 25 meters. Now we need to multiply 50 meters by 25 meters, 50 times 25 which equals 1250. But don’t forget that we’ve also multiplied meters by meters, 55 meters by 25 meters, to find the area of our base. This means that it’s not 1250 alone; it’s 1250 meters squared.

But now we’ve only found the area of the base of this pool; we have not found the volume. To find the volume, we’ll need to take the area of the base of our pool, the area of the bottom of the pool, and multiply it by its height. Or another way to say it, is multiply it by how deep the pool is. The height of our pool, or the depth of our pool, can be found here. This pool is two meters deep, which means we need to multiply the area of the base by two meters. We need to multiply 1250 meters squared by two meters. 1250 multiplied by two equals 2500. Here, we’ve multiplied meters squared by meters, so our volume, the units of our volume, is meters cubed.

The volume of this Olympic-sized pool would be 2500 meters cubed. We found this by multiplying the area of the base of our pool times the height. In this case, our pool is shaped like a rectangle. We multiplied length times width times height. And after we did that, we found 2500 meters cubed to be the volume.

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