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The problem shows two similar solid shapes, A and B. Shape A has a side length of 3 cm, with a given volume of 22 cm³. Shape B has a side length of 6 cm, and we are tasked with finding its volume.

Since the shapes are similar, the volumes of similar solids are proportional to the cube of the ratio of their corresponding side lengths.

### Steps:
1. The ratio of the side lengths of shapes A and B is:
   \[
   \text{Ratio of side lengths} = \frac{6 \, \text{cm}}{3 \, \text{cm}} = 2
   \]

2. The volume of similar shapes scales with the cube of the side length ratio:
   \[
   \text{Volume ratio} = 2^3 = 8
   \]

3. Multiply the volume of shape A by this ratio to find the volume of shape B:
   \[
   \text{Volume of shape B} = 22 \, \text{cm}^3 \times 8 = 176 \, \text{cm}^3
   \]

Thus, the volume of shape B is **176 cm³**.

Would you like more details on this solution or have any other questions?

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Here are 5 related questions to deepen your understanding:
1. What is the formula for the volume of a cube?
2. How does the volume ratio change if the side length ratio changes?
3. Can this method be applied to shapes that aren't cubes but are still similar?
4. What would happen if the shapes were not similar?
5. How can you generalize this process to find the volume of any pair of similar shapes?

**Tip:** The volume ratio of two similar shapes is always the cube of their side length ratio, no matter the shapes' specific forms.

These solid shapes are similar. Find the volume of shape B, given that the side length of shape A is 3 cm and its volume is 22 cm³, while the side length of shape B is 6 cm.

Calculate the volume of shape B based on similar solid shapes. Shape A has a side length of 3 cm and volume 22 cm³, while shape B has a side length of 6 cm. Learn how to use the side length ratio and cube scaling to solve this geometry problem.

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