Question

The base of a solid right pyramid is a square with an edge length of n units. The height of the pyramid is (n-1) units. Which expression represents the volume of the pyramid?

a) Pyramid Volume Formulas
b) Solid Geometry: Pyramid Measurements
c) Calculating Pyramid Volume
d) Geometry of Right Pyramids

Answer 1

The volume of the pyramid is calculated using the formula V = (1/3)n^3 - (1/3)n^2, where n represents the edge length of the square base.

Step-by-step explanation:

Calculating the Volume of a Pyramid

To find the volume of a solid right pyramid with a square base measuring n units on each side and a height of (n-1) units, we can use the formula for the volume of a pyramid, which is V = (1/3) × base area × height. Since the base is a square, the area of the base (A) is n² units. Plugging in the values, our volume formula becomes V = (1/3) × n² × (n-1), which simplifies to V = (1/3)n³ - (1/3)n².