Lesson 7: Surface Area and Volume. Pyramid and Cone

Here is a PDF version of the lesson.

Here is a PDF version of the workbook containing lots of practice.

In this lesson you will learn how to calculate the volume and surface area of the given 3D shapes. Volume is how much space the shape has inside (its capacity). Surface Area is the total outside surface of the shape. 

In order to calculate the volume of a square-based pyramid, we multiply the area of the base by the height of the pyramid. Sometimes, the height is unknown and needs to be determined using the height of the lateral surface and Pythagorean Theorem. 

The process for finding the volume of a cone is similar.

In order to calculate the surface area of any 3D shape, we need to determine the area of all 2D shapes that make up the 3D figure and add them together. Thus, the surface area of a square-based pyramid would be the sum of the areas of 4 triangular faces and the area of a square base.

Depending on the situation, we may need to exclude some of the faces from our calculations (for example, the floor inside the house when determining the area of the walls to be painted, etc.)

Angle relationships short animation