Finding a missing dimension of a prism using the volume formula
About this video
The video finds the height of a prism whose volume is 56 cubic units and whose base is drawn on a grid. Counting squares gives a base area of 12 square units, and solving 56 = 12 × height gives a height of 56/12, which simplifies to 14/3 units.
You'll be able to
- use volume = area of base × height for a prism.
- find a missing height by dividing the volume by the base area.
- simplify a fraction answer by dividing by a common factor.
Key words
- prism
- A 3D shape with two matching bases joined by flat sides.
- volume
- The amount of space a 3D shape takes up, measured in cubic units.
- area of the base
- How many square units cover the bottom face of the prism.
Transcript
- [Instructor] The base of a prism is shown on the grid. That's this right over here. Each square on the grid represents one square unit. The volume of the prism is 56 cubic units. What is the height of the prism? Pause this video, have a go at that. All right, well, we know that the volume of this prism is going to be equal to the area of the base times the height.
Well, we know a few things already. We know that the volume is 56 cubic units, so 56 is going to be equal to the area of the base times the height. Well, what's the area of the base? Well, we can look at this, and actually we could just count the squares. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, so it's equal to 12 times the height.
12 square units is the area of the base. So to figure out the height, we just divide both sides by 12. 12 times what is equal to 56? Divide both sides by 12, and so we get our height is equal to 56 over 12, which is the same thing as, let's see, it looks like both the numerator and the denominator is divisible by four.
So four goes into 56, what is that, 14 times? Yeah, 10 times four is 40 and then another, four times four is 16. So this is 14 over, and if you divide 12 by four, you're going to get three, 14 over three
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