Question

Ethan has partially filled the prism with 8 unit cubes.

A rectangular prism with length, height, and width of 3.
How many more cubes does he need to fill the prism completely?
10
15
19
21

Answer 1

To determine how many more cubes Ethan needs to fill the prism completely, we first need to calculate the total volume of the rectangular prism.

The volume \( V \) of a rectangular prism can be calculated using the formula:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

For this prism:
- Length = 3
- Width = 3
- Height = 3

Calculating the volume:

\[
V = 3 \times 3 \times 3 = 27 \text{ cubic units}
\]

Next, we know that Ethan has already filled the prism with 8 unit cubes. To find out how many more cubes are needed to fill the prism completely, we subtract the number of cubes Ethan has from the total volume:

\[
\text{Cubes needed} = \text{Total volume} - \text{Cubes already in prism}
\]
\[
\text{Cubes needed} = 27 - 8 = 19
\]

Therefore, Ethan needs **19 more cubes** to fill the prism completely.

The answer is **19**.