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?

Answer 1

\frac{n^{2} (n - 1)}{3} \\

Explanation:

1) Using the formula for finding the volume of a pyramid:

A = (1/3)lwh

2) Since the base is a square, the length and width will be the same:

A = (1/3) x n x n x (n-1)

A = \frac{n^{2} (n - 1)}{3} \\

Answer 2

For this case we have that by definition, the volume of a pyramid is given by:

`V = \frac {A_ {b} * h} {3}`

Where:

`A_ {b}:`It is the area of the base

h: It is the height

According to the data we have that the base of the pyramid is square, so its area is:

`A_ {b} = n * n = n ^ 2\\h = n-1`

Substituting we have:

`V = \frac {n ^ 2 * (n-1)} {3}`

Answer:

`V = \frac {n ^ 2 * (n-1)} {3}`