https://file.aiquickdraw.com/mathbot/file/1729344503468rg66mi5a.jpg

The image shows a frustum of a pyramid with the following dimensions:

- The top square has sides of length 15 cm.
- The bottom square has sides of length 18 cm.
- The vertical height of the frustum is 4 cm.

To find important properties of this frustum, we can compute:

1. **Volume of the Frustum**:
   The volume \( V \) of a frustum of a pyramid is given by the formula:
   \[
   V = \frac{1}{3} h (A_1 + A_2 + \sqrt{A_1 A_2})
   \]
   where:
   - \( h \) is the height of the frustum,
   - \( A_1 \) is the area of the top square,
   - \( A_2 \) is the area of the bottom square.

   The areas of the squares are:
   \[
   A_1 = 15^2 = 225 \text{ cm}^2
   \]
   \[
   A_2 = 18^2 = 324 \text{ cm}^2
   \]
   Plugging these into the formula:
   \[
   V = \frac{1}{3} \times 4 \times (225 + 324 + \sqrt{225 \times 324})
   \]
   \[
   V = \frac{4}{3} \times (549 + \sqrt{72900})
   \]
   \[
   V = \frac{4}{3} \times (549 + 270)
   \]
   \[
   V = \frac{4}{3} \times 819 = \frac{3276}{3} = 1092 \text{ cm}^3
   \]

2. **Surface Area** (if needed):
   To compute the surface area, we would calculate the lateral surface area and the areas of the top and bottom faces separately.

Would you like further details or have any specific questions on this calculation? Here are some possible follow-up questions:

1. What is the formula for the lateral surface area of a frustum?
2. How do you calculate the slant height of this frustum?
3. How is the area of the frustum's lateral faces determined?
4. Can this formula be applied to any regular polygon-based frustum?
5. What are practical applications of frustum volume calculations?

**Tip**: For frustums, always verify the type of polygonal base (square, triangular, etc.) before applying area or volume formulas!

What is the volume and surface area of a frustum of a square pyramid with top square sides of 15 cm, bottom square sides of 18 cm, and a vertical height of 4 cm?

Learn how to calculate the volume and surface area of a frustum of a square pyramid. The top square has sides of 15 cm, the bottom square has sides of 18 cm, and the frustum has a vertical height of 4 cm. Includes a step-by-step solution using geometry formulas.

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