Question

a rectangular prism has a volume of 36 cubic units. it has 9 layers of unit cubes. how many unit cubes are in each layer?

Explanation:

Step1: Recall the volume formula for a rectangular prism with unit cubes.

The volume of a rectangular prism made up of unit cubes is equal to the number of unit cubes in each layer multiplied by the number of layers. Let \( n \) be the number of unit cubes in each layer and \( l \) be the number of layers. Then the volume \( V = n\times l \).

Step2: Solve for the number of unit cubes in each layer.

We know that \( V = 36 \) cubic units and \( l = 9 \) layers. We need to find \( n \). From the formula \( V=n\times l \), we can rearrange it to \( n=\frac{V}{l} \). Substituting the given values, we get \( n = \frac{36}{9} \).

Step3: Calculate the value of \( n \).

\( \frac{36}{9}=4 \).

Answer:

4