Answer:
[tex]h=15cm[/tex]
Step-by-step explanation:
- First, let's start off with the equation for the area of a rectangular prism. This first equation I write also applies for cubes, cylinders, and any other shape whose base form does not change as you move up, like a pyramid.
[tex]V=[/tex] area of base × height
- This formula is shown as follows for rectangular prisms and cubes:
[tex]V=lwh[/tex]
[tex]l =[/tex] length
[tex]w=[/tex] width
[tex]h=[/tex] height
- In this problem, the concept of [tex]l[/tex] and [tex]w[/tex] is unnecessary, as the product of their multiplication is already given in the problem, but this is helpful for future reference.
- Let's see what we know:
[tex]V=3000cm^3\\lw=200cm^2[/tex]
[tex]h=[/tex] ?
- Now, plug this into our formula for volume.
[tex]V=lwh\\(3000cm^3)=(200cm^2)(h)[/tex]
- Representing both [tex]l[/tex] and [tex]w[/tex] as one value doesn't matter because you are able to multiply in any order as long as there is no addition or subtraction involved. Let's solve for [tex]h[/tex].
[tex](3000cm^3)=(200cm^2)(h)\\\frac{3000cm^3}{200cm^2}=\frac{(200cm^2)(h)}{200cm^2}[/tex]
- Notice that our units cancel out, leaving us with only [tex]cm[/tex] for our height, as it should be. Linear magnitude has no exponent in the units, 2D magnitude like the area of a flat plane is represented with a square, and 3D magnitude or volume is shown with a cube in the units.
- flat shape ⇒ [tex]cm^2[/tex]
- volumetric shape ⇒ [tex]cm^3[/tex]
- NOW let's finish solving for height.
[tex]\frac{3000cm^3}{200cm^2}=\frac{(200cm^2)(h)}{200cm^2}\\15cm=h[/tex]
