Scale Factor Ratio Similar

The rectangles are similar.

Solve for x.

Mathematical Equivalence

ON

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

_{Line AB corresponds with what line?} 

• XZ

• XY

• YZ

• YX

What is the scale factor of the side lengths of the figure on the left to the figure on the right.

• 3/1

• 3240/120

• 27/1

• 9/1

Are the two figures similar?
(If yes, what is the similarity ratio?)

• Yes; 3

• Yes; 3/10

• Yes; 3/5

• No

The pair of figures is similar. Find the missing side.

• x = 12

• x = 3

• x = 40

• x = 4

Two similar cones have a scale factor of 8/27. What is the ratio of their volumes?

• 2/3

• 64/729

• 512/19683

• 8/27

Two spheres have a scale factor ratio of 1:3.  The smaller sphere has a surface area of 16 ft²_.  Find the surface area of the larger sphere.

• 48 ft²

• 144 ft²

• 432 ft²

• 32 ft²

The volume of a prism is 1000 cubic centimeters. A similar prism has a volume of 27 cubic centimeters. What is the ratio of their surface areas?

• 100:9

• 10:3

• 500:13.5

• 100:2.7

Are the two figures similar?
(If yes, what is the similarity ratio?)

• Yes; 5

• Yes; 9:6

• Yes; 1/3

• No