Proportions and Similar Solids

The video tutorial covers identifying similar solids, explaining that similar solids have the same shape but different sizes, with corresponding linear measurements being proportional. It introduces the concept of scale factors and provides examples of comparing different solids, including pyramids and cylinders, using diagrams and setting up proportions to find missing values.

What is a similar solid?

• A solid with the same shape and size

• A solid with the same size but different shape

• A solid with the same shape but different size

• A solid with different shape and size

Which of the following is NOT a type of linear measurement?

• Length

• Width

• Volume

• Height

In the first example, what is the simplified ratio of the radius of solid A to solid B?

• 1:3

• 3:2

• 3:1

• 2:1

In the second example, why are the solids not similar?

• The heights are not proportional

• None of the ratios are the same

• The widths are not proportional

• The lengths are not proportional

What is the scale factor for the third example where the solids are similar?

• 3:5

• 2:1

• 5:3

• 1:2

Which cylinder is similar to cylinder A and what is the scale factor?

• Cylinder E, scale factor 3:2

• Cylinder B, scale factor 2:3

• Cylinder C, scale factor 3:2

• Cylinder D, scale factor 1:4

Which cylinder is similar to cylinder C and what is the scale factor?

• Cylinder E, scale factor 3:2

• Cylinder D, scale factor 1:4

• Cylinder B, scale factor 1:4

• Cylinder A, scale factor 2:3

In the first proportion example, what is the missing value X if 9/15 = 21/X?

• 45

• 30

• 35

• 40

In the second proportion example, what is the missing value X if 20/16 = X/18?

• 21.5

• 20.5

• 23.5

• 22.5

In the last example, what is the missing value X if 10/24 = X/43.2?

• 36

• 24

• 43.2

• 18