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To solve the problem, we are asked to calculate the volume of a right pyramid with a square base.

### Given:
- The base of the pyramid is a square with side length \( 9 \, \text{m} \).
- The height of the pyramid is \( 6 \, \text{m} \).

### Formula for the volume of a pyramid:
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times \text{Area of the base} \times \text{Height}
\]

### Step 1: Calculate the area of the base
The area of a square is given by:
\[
\text{Area of the base} = \text{side}^2 = 9^2 = 81 \, \text{m}^2
\]

### Step 2: Apply the formula for volume
Now, we substitute the area of the base and the height into the formula for the volume:
\[
V = \frac{1}{3} \times 81 \, \text{m}^2 \times 6 \, \text{m}
\]

### Step 3: Simplify the calculation
\[
V = \frac{1}{3} \times 486 \, \text{m}^3 = 162 \, \text{m}^3
\]

### Answer:
The volume of the pyramid is \( 162 \, \text{m}^3 \).

Thus, the correct choice is:
**D) 162 \( \text{m}^3 \)**.

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you calculate the volume of a pyramid with a triangular base?
2. What is the significance of the height in the formula for the volume of a pyramid?
3. How does the formula for the volume of a pyramid compare to that of a cylinder?
4. If the height of the pyramid were doubled, how would that affect the volume?
5. What are the units of the volume and why?

**Tip:** Remember that the volume of a pyramid is always one-third of the product of the base area and the height, which is why pyramids have less volume than prisms of the same base and height.

Uma pirâmide reta possui base quadrada, com 9 m de lado e 6 m de altura. Qual o volume dessa pirâmide em m³?

Learn how to calculate the volume of a right pyramid with a square base of 9 m and a height of 6 m. This problem demonstrates key geometry concepts such as area and volume calculations. Suitable for students in Grades 9-11.

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