Scale Factor Volume Surface Area

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

If all of the dimensions of a triangular prism decreased by 1/3, how much would the volume decrease by?

• 1/27

• 1/9

• 1/3

• 1/6

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

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 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 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 surface area of a certain pyramid is 54 square meters. Its volume is 648 cubic meters. If a similar pyramid has a volume of 8232 cubic meters, what is its surface area?

• 686 m²

• 168 m²

• 126 m²

• 294 m²

The surface area of a certain prism is 1088 square km and its volume is 13312 cubic km. If a similar solid has a surface area of 425 square km, what is this similar solids volume?

• 3250 cubic km

• 5200 cubic km

• 1950 cubic km

• 8320 cubic km

Two similar cylinders have surface areas of 40π ft² and 90π ft². What is the ratio of the height of the large cylinder to the height of the small cylinder?

• 4/9

• 2/3

• 8/27

• 16/81

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

• Yes; 3

• Yes; 3/10

• Yes; 3/5

• No