top of page
Search

# How to find volume and surface area of pyramids

In this note, you will learn:

· What are pyramids?

. Volume and surface area of pyramids

· Application questions involving volume and surface area of pyramids

Today, we will be learning about pyramids. Pyramids exist all around us, from man-made architectures to everyday objects that we are used to seeing. So, without further ado, let’s begin!

## What are pyramids?

Based on geometrical terms, a pyramid is a polyhedron (a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices) formed by connecting a polygonal base and a point called the apex or vertex.

Note: A polygon is essentially a plane figure that is made up of a finite number of straight-line segments (at least three and above) connected to form a closed polygonal chain.

The number of straight-line segments is typically five or more, because we know that a three-sided polygon is called a triangle, and four-sided polygon is either called a rectangle or a square.

## How to find volume of pyramid?

The general formula to find the volume of a pyramid is:

### V = 1/3 l w h OR V = 1/3 X Base Area X Height

where V is the volume of the pyramid, l is the base length of the pyramid, w is the base width of the pyramid and h is the height of the pyramid

## How to find the surface area of pyramid?

The general formula to find the surface area of a pyramid is:

## Application questions involving volume and surface area of pyramids

### How to find volume of a pyramid

OPQR is a triangular pyramid with a base area of 35 cm^2 and a height of 12 cm. Find the volume of the triangular pyramid.

Solution:

Volume of triangular pyramid = 1/3 X Base Area X Height

= 1/3 X 35 X 12

= 140 cm^3

### How to finding surface area of a pyramid

OJKLM is a pyramid with a square base of length 18 cm. Given that the slant height of the pyramid is 23 cm, find its total surface area.

Solution:

Area of each triangular face = 1/2 X 8 X 23

= 207 cm^2

Area of square base = 18 X 18

= 324 cm^2

Therefore, Total surface area of pyramid = 4 × area of each triangular face + area of square base

= 4 X 207 + 324

= 1152 cm^2

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on these interesting geometrical shapes, their formulae and its application!

If you have any pending questions, please do go on to our Facebook page, Instagram or contact us directly at Math Lobby! We have certified mathematics tutors to aid you in your journey to becoming a better student!

As always: Work hard, stay motivated and I wish all students a successful and enjoyable journey with Math Lobby!

*

*

*