Volume of Rectangular Pyramids

The volume of a rectangular pyramid is given by the formula: $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ .

The base area of a rectangular pyramid is calculated by multiplying the length and width of the base: $$\text{Base Area} = \text{Length} \times \text{Width}$$ .

The height of a pyramid is the perpendicular distance from the base to the apex (top point) of the pyramid.

Volume = $$\frac{1}{3} \times (4 \times 6) \times 3 = 24 \text{ in}^3$$ .

Volume is measured in cubic units, such as cubic inches (in³), cubic feet (ft³), or cubic meters (m³).

If both pyramids have the same height, the volume depends on the base area; a square pyramid with a larger base area will have a greater volume.

Volume = $$\frac{1}{3} \times (5 \times 5) \times 10 = \frac{1}{3} \times 25 \times 10 = \frac{250}{3} \approx 83.33 \text{ cm}^3$$ .

Increasing the height of a pyramid increases its volume, assuming the base area remains constant.

Volume = $$\frac{1}{3} \times 12 \times 4 = 16 \text{ m}^3$$ .

The factor 1/3 accounts for the fact that a pyramid occupies one-third of the space of a prism with the same base area and height.