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The problem asks to determine the volume of the colored solid in the cone depicted in Figure 2. This figure shows a cone, part of which is colored, and we need to compute the volume of that colored section using the provided dimensions.

### Steps to calculate the volume:
1. **Given dimensions**:
   - Radius of the base of the full cone \( r_1 = 1.8 \, \text{m} \)
   - Radius of the smaller top section \( r_2 = 0.6 \, \text{m} \)
   - Full height of the cone \( H = 6 \, \text{m} \)
   - Height of the smaller top section \( h_{\text{top}} = 2 \, \text{m} \)
   - Height of the colored section \( h_{\text{colored}} = 4 \, \text{m} \) (since it's the remaining height after removing the top section).

2. **Volumes**:
   - The volume \( V \) of a cone is given by the formula:
     \[
     V = \frac{1}{3} \pi r^2 h
     \]
   - We need to compute:
     1. The volume of the full cone.
     2. The volume of the smaller cone (top section to be removed).
     3. Subtract the volume of the smaller cone from the volume of the full cone to get the volume of the colored solid.

Let me calculate these volumes for you.The volume of the colored section of the cone is approximately **19.6 cubic meters**.

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How is the formula for the volume of a cone derived?
2. What is the significance of subtracting the smaller cone’s volume from the full cone's volume?
3. How would the volume change if the height of the smaller cone was doubled?
4. Can you calculate the surface area of the colored section of the cone?
5. How does the ratio of the radii of the two cones affect the volume?

**Tip**: When calculating the volume of a truncated cone, you can also use the formula for a frustum instead of subtracting two cone volumes.

Determine the volume of the colored solid in the cone depicted in Figure 2 using the provided dimensions (radius of the base, radius of the smaller top section, full height of the cone, height of the smaller top section, and height of the colored section).

Learn how to calculate the volume of a colored section of a truncated cone using geometry formulas. The problem involves finding the volume of two cones and subtracting the smaller cone's volume from the full cone to determine the volume of the colored solid.

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