Exploring Area and Volume Relationships in Similar Solids

What defines two solids as being similar?

• They are made of the same material.

• They have the same color.

• Their volumes are identical.

• All corresponding linear measurements are proportional.

What is a linear measurement in the context of similar solids?

• A measurement that involves time.

• A measurement such as edge length or radius.

• A measurement of volume.

• A measurement that involves weight.

How is the scale factor related to the surface areas of similar solids?

• The scale factor is irrelevant to surface areas.

• The ratio of the surface areas is the scale factor cubed.

• The ratio of the surface areas is the scale factor squared.

• The scale factor is added to the surface areas.

What is the surface area of the smaller prism given in the example?

• 16 inches squared

• 54 inches squared

• 90 inches squared

• 40 inches squared

What does the ratio of the surface areas of similar solids represent?

• The scale factor added

• The scale factor divided

• The scale factor squared

• The scale factor subtracted

How is the volume of a solid calculated?

• Length times width

• Area of the base times the height

• Area of the base plus the height

• Sum of all edge lengths

What is the ratio of the volumes of the two prisms discussed?

• 3 over 2

• 9 over 4

• 27 over 8

• 54 over 16

How does the ratio of volumes relate to the scale factor?

• It is the scale factor squared.

• It is equal to the scale factor.

• It has no relation to the scale factor.

• It is the scale factor cubed.

What general rule can be derived about the relationship between scale factor and measurements of similar solids?

• Volume ratios are the scale factor added.

• Surface area ratios are the scale factor divided.

• Volume ratios are the scale factor cubed.

• Surface area ratios are the scale factor subtracted.

If you know the ratio of volumes, how can you determine the scale factor?

• By dividing the ratio.

• By squaring the ratio.

• By adding the ratio.

• By taking the cube root of the ratio.