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?
on(n-1) units
on(n-1)2 units
on (n - 1) units
o nº(n-1) units
(n-1)
n
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MA

Answer 1

Volume = ⅓n²(n-1) or ⅓(n³ - n²)

Explanation:

Given

Solid Shape: Right pyramid

Edge= n units

Height= n - 1 units

Required

Volume of the pyramid

The volume of a right pyramid is

Volume = ⅓Ah

Where A represents the area of the base

h represent the height of the pyramid

Since it has a square base;

The area is calculated as follows

Area, A = edge * edge

A = n * n

A = n²

Recall that

Volume = ⅓Ah

Substitute n² for A and n - 1 for h

The expression becomes

Volume = ⅓ * n² * (n - 1)

Volume = ⅓n²(n-1)

The expression can be solved further by opening the bracket

Volume = ⅓(n³ - n²)