https://file.aiquickdraw.com/mathbot/file/1725537007829cr22ggt3.jpg

To solve this problem, we need to calculate the volume of the rock, which is measured by the difference in water levels when the rock is placed in the container.

Here's the step-by-step process:

### 1. Analyze Dimensions from the Image:

- **Without the rock**: The water level is at 4 cm.
- **With the rock**: The water level rises to 7 cm.
  
The base dimensions of the container remain constant: 6 cm (length) and 6 cm (width).

### 2. Calculate the Volume of Water Displaced:
The volume of the displaced water equals the volume of the rock. To find the difference in water height:

\[
\text{Height difference} = 7 \, \text{cm} - 4 \, \text{cm} = 3 \, \text{cm}
\]

The volume of the displaced water (and thus the rock) is:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height Difference}
\]

Substitute the values:

\[
\text{Volume} = 6 \, \text{cm} \times 6 \, \text{cm} \times 3 \, \text{cm} = 108 \, \text{cm}^3
\]

### 3. Conclusion:
The volume of the rock is \(108 \, \text{cm}^3\).

### Answer:
The correct option is \( \boxed{6 \times 6 \times 3} \).

Would you like further details or clarifications?

Here are five related questions to deepen your understanding:
1. How does Archimedes' principle relate to finding the volume of irregular objects?
2. How can we measure the volume of objects that float in water?
3. What is the relationship between volume and density for an object?
4. How would this calculation change if the container were not rectangular?
5. What are other methods to determine the volume of a rock without using water displacement?

**Tip:** Always make sure to account for all given dimensions and compare them before performing volume calculations.

To find the volume of a rock, Gilda places it in a container of water and measures the change in depth. The volume of the rock in cubic centimeters is?

Learn how to calculate the volume of a rock using water displacement with a step-by-step solution. Understand the core concepts of volume, geometry, and Archimedes' principle. Suitable for Grades 6-8.

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