Similar Solids and Missing Lengths

If the ratio of the areas of two similar figures is 64:121, what is the ratio of their volumes?

• 64:121

• 8:11

• 120:242

• 512:1331

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.

• 9 : 25

• 3 : 5

• 1 : 10

• 27 : 125

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.

• 1 : 63

• 7 : 9

• 49 : 81

• 343 : 729

The surface area of a rectangular prism is 166 square feet. A similar prism has a surface area of 1494 square feet. If the length of the smaller prism is 5 feet, what is the length of the larger prism?

• 10

• 15

• 45

• 50

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

The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure.

• SA = 612 km², V = 2160 km³

• SA = 612 km², V = 360 km³

• SA = 3672 km², V = 2160 km³

• SA = 102 km², V = 60 km³

The volumes of two similar solids are in the ratio 27:8

What is the ratio of the surface areas?

• 3:2

• 3:1

• 9:4

• 9:1

A scale factor of 2 is used to enlarge the dimensions of a square. What is the effect of this change on the area of the square?

• The area will be half as big.

• The area will be twice as large.

• The area will be 4 times larger.

• The area will be 8 times larger.

• The area will not change.

Two similar pyramids have heights of 4 inches and 7 inches.  What is the ratio of the volume of the small pyramid to the volume of the large pyramid? 

• 4:7

• 16:49

• 64:343

• 12:21

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

• x = 9

• x = 28

• x = 7

• x = 63