Quiz on Areas and Volumes of Similar Solids

What is the scale factor between two similar pyramids if their altitudes are in the ratio 8:20?

• 4:5

• 5:8

• 2:5

• 1:2

If the scale factor between two similar solids is 2:5, what is the ratio of their lateral areas?

• 1:1

• 4:25

• 8:125

• 2:5

What is the relationship between the scale factor and the volume ratio of two similar solids?

• The volume ratio is the scale factor cubed

• The volume ratio is the scale factor

• The volume ratio is the square root of the scale factor

• The volume ratio is the scale factor squared

In the context of similar solids, what does a scale factor of 1:2 imply about their corresponding linear dimensions?

• They are equal

• One is twice the other

• One is half the other

• They are unrelated

Given a larger cube with a volume of 64 cm³ and a diagonal of 4√3 cm, what is the volume of a smaller cube with a diagonal of 2 cm?

• 8 cm³

• 16 cm³

• 32 cm³

• 64 cm³

What is the scale factor if the diagonal of one cube is 2 cm and the diagonal of another cube is 4√3 cm?

• 1:√2

• 1:2

• 1:√3

• 1:3

If two similar cones have volumes in the ratio 1:8, what is the ratio of their lateral areas?

• 1:4

• 1:16

• 1:2

• 1:8

If the lateral area of a smaller cone is 15π and the scale factor is 1:2, what is the lateral area of the larger cone?

• 15π

• 45π

• 60π

• 30π

How do you determine the scale factor between two similar cones if you know the ratio of their heights?

• Cube the height ratio

• Use the height ratio directly

• Square the height ratio

• Take the square root of the height ratio

How can you prove the ratio of volumes of two similar cones using their scale factor?

• By squaring the scale factor

• By doubling the scale factor

• By cubing the scale factor

• By taking the square root of the scale factor