To find the volume of the pyramid in the image, we can use the formula for the volume of a pyramid:

$V = \frac{1}{3} \times B \times h$

Where:

• $V$ is the volume.
• $B$ is the area of the base.
• $h$ is the height of the pyramid (perpendicular distance from the base to the apex).

Step 1: Calculate the Area of the Base

The base of this pyramid is a rectangle with dimensions:

• Length $l = 8 \, \text{cm}$
• Width $w = 3 \, \text{cm}$

The area of the base $B$ is:

$B = l \times w = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2$

Step 2: Use the Pyramid Volume Formula

The height $h$ of the pyramid is given as $h = 10 \, \text{cm}$.

Now, using the volume formula:

$V = \frac{1}{3} \times 24 \, \text{cm}^2 \times 10 \, \text{cm}$

Let me calculate the result for you.The volume of the pyramid is $80 \, \text{cm}^3$.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. How would the volume change if the height was doubled?
2. What would happen to the volume if the base was a square instead of a rectangle?
3. Can the same formula for the volume be applied to a cone? If so, how?
4. How is the surface area of this pyramid calculated?
5. How would the volume change if the base dimensions were halved?

Tip: For any pyramid, as long as the base is a polygon (not necessarily a rectangle), you can use the same volume formula—just make sure to calculate the correct area of the base.