The video tutorial covers the fundamental theorem of similarity, explaining how similar figures have proportional lengths, areas, and volumes based on a K value. Through various examples, the tutorial demonstrates how to calculate and compare these properties in different scenarios, such as squares, airplane models, pyramids, scale models, and pizzas. The focus is on understanding the application of K, K squared, and K cubed in real-world problems.

What does the fundamental theorem of similarity state about the relationship between the lengths of similar figures?

• Their lengths are equal.

• Their lengths are unrelated.

• Their lengths are proportional to a single K value.

• Their lengths are inversely proportional.

In the example problem, what is the K value when comparing the side lengths of the two squares?

• 1/2

• 2/1

• 12/5

• 5/12

How do you calculate the area comparison between two similar figures?

• By cubing the K value.

• By squaring the K value.

• By using the K value directly.

• By taking the square root of the K value.

When comparing the wingspans of two similar airplane models, what is the K value if the larger model is 180 cm and the smaller is 90 cm?

• 1/2

• 2

• 1

• 3

What is the K squared value when comparing the areas of the tail pieces of the airplane models?

• 1

• 4

• 8

• 2

For similar pyramids, if the K value is 3/2, what is the K cubed value used for volume calculations?

• 9/4

• 3/2

• 8/27

• 27/8

If the volume of the smaller pyramid is 100 cubic inches, what is the volume of the larger pyramid using a K cubed value of 27/8?

• 337.5 cubic inches

• 8 cubic inches

• 100 cubic inches

• 27 cubic inches

In a scale model that is 1/15th the size of the original, what is the K cubed value for comparing weights?

• 1/15

• 1/225

• 1/3375

• 1/375

How does the amount of paint needed for a scale model compare to the original object?

• It is inversely proportional to K squared.

• It is the same.

• It is proportional to K squared.

• It is proportional to K cubed.

If a 16-inch pizza costs $1.50 in ingredients, what is the cost for a 12-inch pizza using a K squared value of 9/16?

• $2.00

• $0.75

• $1.50

• $1.13