Similar Solids
Easily Explained with 12 Examples!

In this geometry lesson, you’re going to learn all about similar solids.

Do you know the key to determine the volume and surface area of similar solids?

It’s the scale factor.

Let’s find out why!

We already know that two polygons are similar if all of their corresponding angles are congruent and their side lengths are proportional, but what about similar solids?

Similar solids are those that have the same shape but not the same size, which means corresponding segments are proportional and corresponding faces are similar polygons.

Thus, two solids with equal ratios of corresponding linear measure are called similar solids, and the COMMON RATIO is called the SCALE FACTOR of one solid to the other solid.

In other words, to prove that two solids are similar, we must show corresponding heights, widths, lengths, radii, etc., to be proportional, as ck-12 accurately states.

Additionally, the surface area and volume of similar solids have a relationship related to the scale factor.

The Similar Solids Theorem tells us that if two similar solids have a scale factor, then the corresponding areas and volumes have the following ratios:

For example, take the two rectangular prisms below. The scale factor for side lengths is 1:3, meaning the larger prism is 3 times the size of the smaller prism. Therefore, we can find the ratios for area and volume for these two solids using the Similar Solids Theorem.

Next, in the video lesson, you’ll learn how to tackle harder problems, including:

1. Determine whether two solids are similar by finding scale factors, if possible.
2. Use the similar solids theorem to find the surface area and volume of similar solids.
3. Use a scale factor of a similar solid to find the missing side lengths.

Video – Lesson & Examples

58 min

• Introduction
• 00:00:28 – Determine if the solids are similar (Examples #1-5)
• 00:11:32 – Similar solids theorem
• Exclusive Content for Member’s Only

• 00:13:31 – Find the surface area and volume of the larger solid given the scale factor (Examples #6-8)
• 00:26:04 – Find the scale factor for the similar solids (Examples #9-11)
• 00:38:51 – Find the missing side lengths given the scale factor for two similar solids (Example #12)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions