Volume of a Square Pyramid Formula

A pyramid is a three-dimensional polyhedron with a polygonal base and three or more triangle-shaped faces that meet above the base. The faces are the triangle sides, while the apex is the point above the base. The base is connected to the peak to form a pyramid. When the pyramid’s base is in the shape of a square, the pyramid is called a square pyramid. One square base and three triangular faces make up a square pyramid. It contains 8 edges, 5 vertices, and 4 faces, in other words.

Volume of a Square Pyramid Formula

The space contained between the five faces of a square pyramid is referred to as its volume. Knowing the base area and height of a square pyramid is all that is required to calculate its volume. The volume of a square pyramid is equal to one-third of the product of the base’s area and the pyramid’s height.

Formula

V = (1/3) × a² × h

where,

a is the length of the square base,

h is the height (or altitude).

Sample Problems

Problem 1. Find the volume of a square pyramid if the length of its base is 6 cm and its height is 4 cm.

Solution:

We have, a = 6 and h = 4.

Using the formula we have,

V = (1/3) × a² × h

= (1/3) × 6² × 4

= (1/3) × 36 × 4

= 12 × 4

= 48 cm³

Problem 2. Find the volume of a square pyramid if the length of its base is 12 cm and the height is 15 cm.

Solution:

We have, a = 12 and h = 15.

Using the formula we have,

V = (1/3) × a² × h

= (1/3) × 12² × 15

= (1/3) × 144 × 15

= 144 × 5

= 720 cm³

Problem 3. Find the length of the base of a square pyramid if its volume is 1125 cm³ and height is 15 cm.

Solution:

We have, V = 1125 and h = 15.

Using the formula we have,

V = (1/3) × a² × h

=> 1125 = (1/3) × a² × 15

=> 1125 = (1/3) × a² × 15

=> 1125 = 5a²

=> a² = 225

=> a = 15 cm

Problem 4. Find the height of a square pyramid if its volume is 1372 cm³ and base length is 14 cm.

Solution:

We have, V = 1372 and a = 14.

Using the formula we have,

V = (1/3) × a² × h

=> 1372 = (1/3) × 14 × 14 × h

=> 1125 = (1/3) × 196 × h

=> 196 h = 4116

=> h = 21 cm

Problem 5. Find the area of the base of a square pyramid if its volume is 98 cm³ and height is 6 cm.

Solution:

We have, V = 98 and h = 6.

Using the formula we have,

V = (1/3) × a² × h

=> 98 = (1/3) × a² × 6

=> 98 = 2a²

=> a² = 49 sq. cm