Find the volume of the following rectangular pyramid with a height of 8 inches and a base area of 116 square inches.

To find the volume of a rectangular pyramid, you can use the following formula:

Volume = (1/3) × Base Area × Height

Given the base area is 116 square inches and the height is 8 inches, you just need to substitute those values into the formula.

Volume = (1/3) × 116 in² × 8 in

Now multiply the base area by the height:

116 in² × 8 in = 928 in³

Then divide by 3 to get the volume of the pyramid:

928 in³ ÷ 3 ≈ 309.33 in³

Therefore, the volume of the rectangular pyramid is approximately 309.33 cubic inches.

Extra: Understanding the concepts:

- The volume of a pyramid: It measures how much space the pyramid occupies and is often measured in cubic units (like cubic centimeters, cubic inches, etc.). For a pyramid, the volume is always one-third of the product of the base area and height because the pyramid is essentially a pointed structure that tapers off from its base. - Base Area: This is the area of the base of the pyramid. For a rectangular pyramid, the base area would be the area of the rectangle at the bottom of the pyramid. In our example, it was given as 116 square inches.

- Height: It's the perpendicular distance from the base to the apex (tip) of the pyramid. It's important to use the perpendicular height when calculating the volume and not the slanted height along the side of the pyramid.

- Rectangular Pyramid: This is a type of pyramid with a rectangle for its base hence its volume depends on the area of that rectangle. Keep in mind that pyramids can have other shapes for bases, like triangular pyramids (tetrahedrons) or even irregular shapes, which would alter how their base area is calculated.