Surface Areas and Volumes of Prisms

Two similar prisms have areas of 112 cm squared and 252 cm squared. What is the ratio of their volumes?

Small: large

​ (a)   : ​ (b)  

• 8

• 27

• 4

• 9

• 64

• 729

Farmer Fred has a silo that looks like the one in the picture. The cylinder part is 20 feet tall with a radius of 6 feet. What is the volume of the entire silo? Round to the nearest whole number.

• 3167 ft³

• 2337 ft³

• 2413 ft³

• 2714 ft³

Two similar rectangular prisms have a surface area of 240 square meters and 735 square meters. If the volume of the larger prism is 10290 cubic meters, what is the volume of the smaller prism?

Mathematical Equivalence

ON

Monica got a new fish tank 5 times larger than her old one. The surface area of this tank is ​ (a)   larger than her old one.

• 25 times

• 10

• 5

• 125

• 15

By what factor would the volume of a triangular prism decrease if the dimensions (side lengths) were decreased by a factor of 1/3?

• 1/3

• 1/6

• 1/9

• 1/27

The cylinders shown are similar. If the volume of the larger cylinder is 562.5 m³, then what is the volume of the smaller cylinder?

• 288 m³

• 112.5 m³

• 450 m³

• 360 m³

The cylinders shown are similar. Find the missing height of the larger cylinder.

• 192 cm

• 8 cm

• 48 cm

• 36 cm

Two similar rectangular prisms have widths of 30 centimeters and 50 centimeters. If the larger prism has a volume of 812.5 cm³, then what is the volume of the smaller prism?

• 1354.17 cm³

• 487.5 cm³

• 175.5 cm³

• 292.5 cm³

Two rectangular prisms are similar. The smaller prism has a volume of 24 in³ and the larger prism has a volume of 375 in³. What is the ratio of the surface area of the smaller prism to the surface area of the larger prism?

• 2/5

• 4/25

• 8/125

• 24/375

Which of the following measurements are related to the scale factor? Check all that apply.

• surface areas

• heights

• side lengths

• volume

• perimeter