Lesson 12.6: Changing Dimensions of 3-D Figures Answers

The rectangular prisms shown are similar.

A triangular prism has an equilateral base with each side of the triangle measuring 8.4 centimeters. The height of the prism is 10.2 centimeters. Which triangular prism is similar to the described prism?

The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.

A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm.The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism?

Two similar pyramids have base areas of 12.2 cm2 and 16 cm2. The surface area of the larger pyramid is 56 cm2.What is the surface area of the smaller pyramid?

A cube has an edge length of 9 centimeters.

The volumes of two similar solids are 210 m3 and 1,680 m3. The surface area of the larger solid is 856 m2.What is the surface area of the smaller solid?

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

A shipping box in the shape of a cube has an edge length of 8 inches. It can hold 8 mugs with no extra space between them.

A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side. If the length and width of the base are doubled, how many cubes could the new box hold?

The volume of a triangular prism is increased by a factor of 8.By what factor is the surface area of the figure increased?

The surface area of a rectangular prism is increased by a factor of 16.By what factor is the volume of the figure increased?

Two spheres have volumes of 8π cm3 and 64π cm3. If the surface area of the smaller sphere is 16π cm2, what is the surface area of the larger sphere?

A square pyramid has a base side length of 20.4 cm and a height of 18.2 cm. Which square pyramid is similar?