Question

What is the volume of a rectangular prism with 2 columns of 4 rows each and each cube has an edge length of 15 centimeters?

Answer 1

To find the volume of the rectangular prism consisting of cubes, we first need to determine the dimensions of the prism based on the arrangement of the cubes.

Since there are 2 columns and 4 rows, we can visualize this as follows:

1. The number of cubes in the width (columns) is 2.
2. The number of cubes in the height (rows) is 4.
3. Each cube is a cube with an edge length of 15 cm.

Now we can determine the dimensions of the rectangular prism:

- Width = Number of columns \( \times \) Edge length = \( 2 \times 15 = 30 \) cm
- Height = Number of rows \( \times \) Edge length = \( 4 \times 15 = 60 \) cm
- Depth = Edge length of cube = 15 cm (since each cube has the same edge length)

Now, we can calculate the volume \( V \) of the rectangular prism using the formula for the volume of a prism:

\[
V = \text{Width} \times \text{Height} \times \text{Depth}
\]

Substituting the dimensions into the formula:

\[
V = 30 \, \text{cm} \times 60 \, \text{cm} \times 15 \, \text{cm}
\]

Now perform the multiplication step-by-step:

1. \( 30 \times 60 = 1800 \) cm²
2. \( 1800 \times 15 = 27000 \) cm³

Therefore, the volume of the rectangular prism is:

\[
\boxed{27000} \, \text{cm}^3
\]