Question

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?

Answer 1

`h=15cm`

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.

`V=` area of base × height

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

`V=lwh`

`l =` length

`w=` width

`h=` height

• In this problem, the concept of
  `l` and
  `w` 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:

`V=3000cm^3\\lw=200cm^2`

`h=` ?

• Now, plug this into our formula for volume.

`V=lwh\\(3000cm^3)=(200cm^2)(h)`

• Representing both
  `l` and
  `w` 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
  `h`.

`(3000cm^3)=(200cm^2)(h)\\(3000cm^3)/(200cm^2)=((200cm^2)(h))/(200cm^2)`

• Notice that our units cancel out, leaving us with only
  `cm` 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 ⇒
  `cm`

• flat shape ⇒
  `cm^2`

• volumetric shape ⇒
  `cm^3`

• NOW let's finish solving for height.

`(3000cm^3)/(200cm^2)=((200cm^2)(h))/(200cm^2)\\15cm=h`