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calculate the volume of the square based pyramid below. give answer in cm^3 and give any decimals to nearest whole number

To calculate the volume of the square-based pyramid, we use the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

Where:
- The base area is the area of the square base.
- The height is the perpendicular height of the pyramid.

### Step 1: Calculate the base area
The base of the pyramid is a square, and we are given that one side of the base is \( 38 \, \text{cm} \).

\[
\text{Base Area} = 38 \, \text{cm} \times 38 \, \text{cm} = 1444 \, \text{cm}^2
\]

### Step 2: Use the height of the pyramid
The height of the pyramid is given as \( 45 \, \text{cm} \).

### Step 3: Calculate the volume
Now, substitute the base area and height into the volume formula:

\[
V = \frac{1}{3} \times 1444 \, \text{cm}^2 \times 45 \, \text{cm}
\]

Let's calculate this.The volume of the square-based pyramid is approximately \( 21,660 \, \text{cm}^3 \) when rounded to the nearest whole number.

Do you have any questions or would you like further details? Here are five related questions to expand your understanding:

1. How do you calculate the surface area of this square-based pyramid?
2. What is the slant height of the pyramid, and how can it be calculated using the given dimensions?
3. Can this formula for volume be applied to other types of pyramids, such as a triangular-based pyramid?
4. How would the volume change if the height of the pyramid was doubled but the base remained the same?
5. How do you convert the volume from cubic centimeters to liters?

**Tip:** When working with geometric shapes, visualizing the dimensions and knowing the key formulas helps simplify the process of calculating volume or surface area.

Learn how to calculate the volume of a square-based pyramid with a base side of 38 cm and a height of 45 cm. Using geometry concepts and volume formulas, this problem is suitable for students in Grades 8-10. Find the answer in cubic centimeters rounded to the nearest whole number.

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