Question

Roxanne is going to build a rectangular prism out of 36 one- inch cubes. She wants the height of the rectangular prism to be 3 inches, and she wants the width to be shorter than the length. How many rectangular prisms with different dimensions can she build?

Answer 1

3

Explanation:

Since Roxanne has 36 one inch cubes, the maximum volume of rectangular prism she can have is 36 in³ = 1 in × 1 in × 36 in.

Now, if Roxanne wants a rectangular prism with height 3 inches, this implies that the area of its base is 36 in³/3 in = 12 in².

We now find all the factors of 12 = 1 × 12, 2 × 6, 3 × 4.

So, we have 3 different areas of base of rectangular prism in which the width is shorter than its length the width being the smaller dimension.

So, the different rectangular prisms in which the volume = 36 in³ in which the width is shorter than its length and has a height of 3 in is

1 × 12 × 3, 2 × 6 × 3, 3 × 4 × 3.

So we have 3 different rectangular prisms