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The question shown in the image is about finding the volume of a truncated pyramid as a fraction of the original pyramid's volume. Here’s how we can approach this:

### Given Data:
1. The volume \( V \) of a pyramid with height \( h \) and base area \( A \) is given by:
   \[
   V = \frac{1}{3} A h
   \]
2. In this case, the square pyramid is truncated by removing the top 10 cm.

### Solution Steps:
1. **Determine the Volume of the Original Pyramid:**
   Let’s call the height of the original pyramid \( H \), and assume its base area is \( A \).

   \[
   V_{\text{original}} = \frac{1}{3} A H
   \]

2. **Determine the Volume of the Smaller Pyramid (Removed Section):**
   Since the pyramid is truncated by 10 cm, the height of the smaller (removed) pyramid is 10 cm. Assuming the original pyramid’s height is twice the removed section's height (i.e., \( H = 20 \) cm), the base area of the smaller pyramid will be scaled down by a factor of \((\frac{10}{20})^2 = \frac{1}{4}\).

   So, the volume of the smaller pyramid \( V_{\text{small}} \) will be:
   \[
   V_{\text{small}} = \frac{1}{3} \left(\frac{A}{4}\right) \cdot 10 = \frac{1}{12} A H
   \]

3. **Calculate the Volume of the Truncated Pyramid:**
   The volume of the truncated pyramid \( V_{\text{truncated}} \) is the original pyramid’s volume minus the smaller pyramid’s volume:
   \[
   V_{\text{truncated}} = V_{\text{original}} - V_{\text{small}} = \frac{1}{3} A H - \frac{1}{12} A H = \frac{1}{4} A H
   \]

4. **Express as a Fraction of the Original Volume:**
   Now, the fraction of the original volume is:
   \[
   \frac{V_{\text{truncated}}}{V_{\text{original}}} = \frac{\frac{1}{4} A H}{\frac{1}{3} A H} = \frac{3}{4}
   \]

### Answer:
The correct answer is:
- **Option 3:** \( \frac{3}{4} \)

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Would you like further details on the calculations or explanation? 

Here are 5 related questions that build on this concept:

1. How would the answer change if the original pyramid had a different height?
2. How do you calculate the volume of a truncated cone instead of a pyramid?
3. What is the formula for the volume of a frustum in general?
4. How does scaling affect the area and volume in three-dimensional shapes?
5. What happens to the volume fraction if the removed height was different, say 5 cm instead of 10 cm?

**Tip:** Remember that the volume of similar shapes scales with the cube of the ratio of their corresponding dimensions.

What is the volume of the truncated pyramid as a fraction of the original pyramid's volume?

Learn how to find the volume of a truncated pyramid as a fraction of the original pyramid’s volume. The problem involves understanding volume calculations for pyramids, applying the formula V = (1/3) * A * h, and using proportional reasoning. Ideal for Grade 10 geometry students.

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