Question Video: Finding the Height of a Rectangular prism in a Real-World Context Mathematics • 6th Grade

Given that 405 cm³ of water is poured into a rectangular-prism-shaped vessel with a square base whose side length is 9 cm, find the height of water in the vessel.

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Video Transcript

Given that 405 cubic centimeters of water is poured into a rectangular-prism-shaped vessel with a square base whose side length is nine centimeters, find the height of water in the vessel.

In his question, we’ve been given some information about the volume of water being poured into a rectangular-prism-shaped vessel. This vessel has a square base with side length of nine centimeters. So let’s sketch this out. Here is this vessel. Now, we don’t know what the height of the water is in the vessel when it’s poured in. So, let’s call that ℎ centimeters. We do know that the amount of space this takes up in three dimensions is 405 cubic centimeters. And we also know that this is the volume. And the volume of a cuboid is equal to the area of its base multiplied by its perpendicular height.

Now, we can calculate the area of the base of our vessel. It’s simply a square. So, its area is nine multiplied by nine, which is 81. We’re working in centimeters. So, the area of the base of our vessel is 81 square centimeters. We, in fact, also know that the volume of our water is 405 cubic centimeters. And we’ve said that its height is equal to ℎ.

We can, therefore, form an equation in ℎ. We can say that 405, remember, that’s the volume, is equal to the area of the base, that’s 81, times ℎ or 405 equals 81ℎ. We want to solve for ℎ. So, we’re going to divide both sides of our equation by 81. That gives us ℎ is equal to five. And we can, therefore, say that the height of water in the vessel is five centimeters.

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