Understanding Similar Solids

What is the defining characteristic of similar solids?

• They have the same volume.

• They have the same surface area.

• They are of the same type with equal ratios of corresponding measures.

• They are made of the same material.

What is the scale factor in the context of similar solids?

• The difference in height between the solids.

• The ratio of the volumes of the solids.

• The ratio of corresponding linear dimensions of the solids.

• The ratio of the surface areas of the solids.

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

• It is the square of the scale factor.

• It is the cube of the scale factor.

• It is the same as the scale factor.

• It is the square root of the scale factor.

In the example with rectangular prisms, what was the scale factor between the first and third prism?

• 2/3

• 1/2

• 4/5

• 3/4

Why were the two cones in the example not considered similar?

• They did not have the same scale factor.

• They had different volumes.

• They were made of different materials.

• They had different surface areas.

What is the ratio of the volumes of two similar cylinders with volumes 12π and 324π?

• 1/9

• 1/27

• 1/3

• 1/81

How do you find the scale factor from the ratio of volumes?

• Divide the ratio by the scale factor.

• Multiply the ratio by itself.

• Take the cube root of the ratio.

• Take the square root of the ratio.

If the scale factor between two similar solids is 3:2, what is the ratio of their surface areas?

• 6:4

• 27:8

• 9:4

• 3:2

What is the volume of a solid B if the scale factor is 2:1 and the volume of solid A is 1728?

• 1728

• 864

• 432

• 216

In the advanced example, what is the surface area of solid B if the scale factor is 4:7 and the surface area of solid A is 64π?

• 196π

• 128π

• 256π

• 343π