Question

If there are 6 of 1/3 inch cubes, 1 cube wide and 3 cubes lengthen and 2 cubes height, what’s is the number of cubic inches in the right rectangular prism, enter the answer in a fraction and do not reduce

Answer 1

To find the volume of the right rectangular prism, we first need to determine its dimensions based on how many cubes fit into it.

- Width: 1 cube wide, with each cube measuring \( \frac{1}{3} \) inch, so the width is:
\[
1 \times \frac{1}{3} = \frac{1}{3} \text{ inches}
\]

- Length: 3 cubes long, so the length is:
\[
3 \times \frac{1}{3} = 1 \text{ inch}
\]

- Height: 2 cubes high, so the height is:
\[
2 \times \frac{1}{3} = \frac{2}{3} \text{ inches}
\]

Now we can calculate the volume \( V \) of the rectangular prism using the formula \( V = \text{width} \times \text{length} \times \text{height} \):
\[
V = \left(\frac{1}{3}\right) \times 1 \times \left(\frac{2}{3}\right)
\]

Calculating this step-by-step:
1. Multiply \( \frac{1}{3} \times 1 = \frac{1}{3} \).
2. Then multiply \( \frac{1}{3} \times \frac{2}{3} = \frac{2}{9} \).

Thus, the volume of the right rectangular prism is:
\[
\frac{2}{9} \text{ cubic inches}
\]

The answer in a fraction without reduction is:
\[
\frac{2}{9}
\]