To solve this problem, let's analyze the information given and apply the formula for the volume of a pyramid.

The formula for the volume of a pyramid is: $V = \frac{1}{3} B h$ where $B$ is the area of the base of the pyramid, and $h$ is the height.

Step-by-Step Solution

1. Identify the Base of the Pyramid: The base of this pyramid is a triangle with a base of 6 inches and a height of 5 inches.

2. Calculate the Area of the Base (B): The area $B$ of a triangle is given by: $B = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the given values: $B = \frac{1}{2} \times 6 \times 5 = 15 \text{ square inches}$

3. Identify the Height (h) of the Pyramid: The height of the pyramid is given as 8 inches.

4. Calculate the Volume (V): Now, plug $B = 15$ and $h = 8$ into the volume formula: $V = \frac{1}{3} \times 15 \times 8 = \frac{1}{3} \times 120 = 40 \text{ cubic inches}$

Answer

The volume of the pyramid is $40$ cubic inches.

Would you like more details or have any other questions?

Here are five related questions to deepen understanding:

1. How would the volume change if the height of the pyramid were doubled?
2. What is the effect on the volume if the base's dimensions are increased by a factor of 2?
3. How is the volume affected if the height remains the same but the base is changed to a different shape?
4. Can the formula for the volume of a pyramid apply to any type of base, not just triangular ones?
5. How would you calculate the volume if the pyramid were only partially filled?

Tip: Always ensure that the units of all dimensions match when calculating volume.