Question

Length:
1 1/3 inches = 4/3 inches
Width: 1 inch
Height: 2/3 inch

How many 1/3 -inch cubes would fit inside the right rectangular prism? (1 point)

Responses 7 cubes 7 cubes 12 cubes 12 cubes 48 cubes 48 cubes 24 cubes

Answer 1

To determine how many \( \frac{1}{3} \)-inch cubes fit inside the rectangular prism, we first need to calculate the volume of the prism and the volume of a single cube.

### Step 1: Calculate the Volume of the Rectangular Prism

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

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

From the problem, we have:

- Length = \( \frac{4}{3} \) inches
- Width = \( 1 \) inch
- Height = \( \frac{2}{3} \) inches

Now plug in the values:

\[
V = \left(\frac{4}{3}\right) \times 1 \times \left(\frac{2}{3}\right)
\]

Calculating it step by step:

\[
V = \frac{4}{3} \times 1 = \frac{4}{3}
\]
\[
V = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \text{ cubic inches}
\]

### Step 2: Calculate the Volume of a \( \frac{1}{3} \)-Inch Cube

The volume of a cube with a side length of \( \frac{1}{3} \) inch is:

\[
V_{\text{cube}} = \text{side}^3 = \left(\frac{1}{3}\right)^3 = \frac{1}{27} \text{ cubic inches}
\]

### Step 3: Divide the Volume of the Rectangular Prism by the Volume of One Cube

To find how many \( \frac{1}{3} \)-inch cubes fit inside the prism, we divide the volume of the prism by the volume of one cube:

\[
\text{Number of cubes} = \frac{V_{\text{prism}}}{V_{\text{cube}}} = \frac{\frac{8}{9}}{\frac{1}{27}}
\]

When dividing by a fraction, we multiply by its reciprocal:

\[
\text{Number of cubes} = \frac{8}{9} \times \frac{27}{1} = \frac{8 \times 27}{9} = \frac{216}{9} = 24
\]

### Conclusion

The number of \( \frac{1}{3} \)-inch cubes that would fit inside the right rectangular prism is \( \boxed{24} \).