Cube A has a volume of 2 in. Cube B has a volume of 9 in. Which of the following expresses the ratio of the side length of Cube A to the side length of Cube B?

(A) 2$: 33

(B) 35 : 2รี

(0) 35:28

(D) 2$: 33

(E) 95 : 25

To find the ratio of the side lengths of Cube A and Cube B, we first need to calculate the side lengths using their volumes.

1. **Volume of a cube formula**: $ V = s^3 $, where $ s $ is the side length.
2. **For Cube A**:
   - Volume = 2 in³
   - $ s_A = \sqrt[3]{2} $

3. **For Cube B**:
   - Volume = 9 in³
   - $ s_B = \sqrt[3]{9} = 3 $

Next, we express the ratio of the side lengths:

\[
\text{Ratio} = \frac{s_A}{s_B} = \frac{\sqrt[3]{2}}{3}
\]

To express this ratio in a simpler form, we can rewrite it as:

\[
\text{Ratio} = \frac{\sqrt[3]{2}}{3} = \frac{2^{1/3}}{3}
\]

Now let's calculate this ratio numerically:

\[
\sqrt[3]{2} \approx 1.26 \quad \text{(to two decimal places)}
\]
\[
\frac{1.26}{3} \approx 0.42
\]

To express this as a ratio of integers, we can multiply both the numerator and the denominator by 3 to avoid fractions:

\[
\frac{1.26 \times 3}{3 \times 3} = \frac{3.78}{9} \approx \frac{2}{5} \text{ (approximately)}
\]

However, the options given do not reflect exact values. Instead, we can analyze the expression $ \frac{\sqrt[3]{2}}{3} $ as a ratio.

Given the options presented, none seem to match the calculation perfectly. However, if we analyze the numerical values, we find:

- $ s_A \approx 1.26 $
- $ s_B = 3 $

This suggests a rough ratio of approximately $ 1:2.4 $, which can be expressed as $ 2:5 $.

Thus, the correct answer appears to be based on an estimation. 

If your question relates to matching this with the options provided, please check if any options are closer numerically.

### Summary
The ratio of the side lengths of Cube A to Cube B is approximately $ 2:5 $ based on calculations.

Would you like any further details or clarifications on this? Here are some related questions you might consider:

1. How do you calculate the side length of a cube from its volume?
2. What is the importance of understanding ratios in geometry?
3. Can you calculate the volumes of other cubes with different side lengths?
4. How does the volume change if the side length is doubled?
5. What are the implications of comparing volumes and surface areas in geometry?

**Tip:** Always check if the dimensions are given in consistent units before performing calculations.

Learn how to determine the ratio of side lengths between two cubes with given volumes. This geometry problem involves using the cube volume formula to find side lengths and expressing their ratio. Suitable for Grades 6-8 students.

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