https://file.aiquickdraw.com/mathbot/file/1728048107609xkbhqo7s.jpg

The image shows a pyramid with a rectangular base, where the base dimensions are 12 units and 10 units, and the height of the pyramid is 8 units. The question is asking to calculate the volume of this pyramid.

The formula for the volume of a pyramid is:

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

1. **Base Area**:
   The base is a rectangle with dimensions 12 units and 10 units. So, the area of the base is:
   \[
   \text{Base Area} = 12 \times 10 = 120 \text{ square units}
   \]

2. **Height**:
   The height of the pyramid is given as 8 units.

3. **Volume Calculation**:
   Now, substitute the base area and the height into the volume formula:
   \[
   V = \frac{1}{3} \times 120 \times 8 = \frac{1}{3} \times 960 = 320 \text{ cubic units}
   \]

So, the volume of the pyramid is **320 cubic units**, which matches the value shown in the box in the image.

Would you like more details on the steps, or have any questions?

Here are 5 related questions to explore further:
1. How would the volume change if the height of the pyramid were doubled?
2. What is the formula for the surface area of a pyramid with a rectangular base?
3. How does the volume formula differ for a cone?
4. Can you find the slant height of the pyramid if the diagonal of the base is needed?
5. What is the effect on volume if the base area is halved but the height remains the same?

**Tip:** Always remember that the volume of a pyramid involves multiplying by \(\frac{1}{3}\), which accounts for its tapered shape compared to a prism with the same base and height.

Calculate the volume of the pyramid with a rectangular base of 12 units by 10 units, and a height of 8 units. The volume is given as 320 cubic units.

Learn how to calculate the volume of a pyramid with a rectangular base of 12 units by 10 units and a height of 8 units. This detailed solution walks through the formula V = (1/3) × Base Area × Height to reach a volume of 320 cubic units. Suitable for students in Grades 8-10.

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