To calculate the volume of the rectangular-based pyramid shown in the diagram:

Step 1: Formula for the volume of a pyramid

The formula to calculate the volume of a pyramid is:

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

Step 2: Calculate the base area

The base of the pyramid is a rectangle with dimensions $5 \, \text{cm}$ by $8 \, \text{cm}$. The area of the base is:

$\text{Base Area} = 5 \times 8 = 40 \, \text{cm}^2$

Step 3: Identify the height

The height of the pyramid is given as $27 \, \text{cm}$.

Step 4: Substitute into the formula

Substitute the base area and the height into the volume formula:

$V = \frac{1}{3} \times 40 \times 27$

$V = \frac{1}{3} \times 1080 = 360 \, \text{cm}^3$

Final Answer:

The volume of the pyramid is:

$\boxed{360.0 \, \text{cm}^3}$

Let me know if you'd like further clarifications or have any other questions!

Related Questions:

1. What is the formula to calculate the surface area of a pyramid?
2. How does the volume of a pyramid change if the height is doubled?
3. How can the slant height be used to calculate the lateral surface area?
4. What is the relationship between the base area and the volume of the pyramid?
5. Can this formula be applied to pyramids with non-rectangular bases?

Tip:

When solving geometry problems, always double-check the given dimensions and ensure the formula aligns with the specific shape.