9. A rectangular prism has a base with an
area of 200 cm2. The volume of the prism is
3,000 cm3. What is the height of the prism?

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.

area of base × height

This formula is shown as follows for rectangular prisms and cubes:

length

width

height

In this problem, the concept of and 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:

?

Now, plug this into our formula for volume.

Representing both and 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 .

Notice that our units cancel out, leaving us with only 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. line ⇒ flat shape ⇒ volumetric shape ⇒ NOW let's finish solving for height.

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