Question

type the correct answer in the box. use numbers instead of words.
the right rectangular prism shown is filled with one layer of unit cubes. it can fit a total of 3 layers of unit cubes. each cube represents 1 cubic foot.

$v = l \times w \times h$ or $v = b \times h$

what is the volume of the right rectangular prism?
the volume is \\(\square\\) cubic feet.

Explanation:

Step1: Find the number of unit cubes in one layer

Looking at the base (one layer) of the right rectangular prism, we can count the number of unit cubes. From the diagram, we can see that the length (number of cubes along one side) is 6 and the width (number of cubes along the other side of the base) is 4. So the number of unit cubes in one layer is \( 6\times4 = 24 \) (since the area of the base \( b=l\times w \), and here each cube is 1 cubic foot, so the number of cubes in one layer is the area of the base in square feet, but since each cube is 1 cubic foot, it's also the number of cubic feet in one layer).

Step2: Find the total volume with 3 layers

Since there are 3 layers of unit cubes, and each layer has 24 unit cubes (each representing 1 cubic foot), the total volume \( V \) is the number of unit cubes in one layer multiplied by the number of layers. So \( V = 24\times3 = 72 \).

Answer:

72