Similar 3-D Solids

Given similar solids with surface areas of 400 m² and 25 m².

Match the following:

• 1/16

• Their Ratio of Surface Areas

• 1/4

• Their Ratio of Volumes

• 1/64

• Their Scale Factor

A small cone has a radius of 3 cm and a height of 4 cm.

If a larger cone is similar to the small cone and their scale factor is 3,

then the radius of the larger cone = ___ cm

Two similar rectangular prisms have a scale factor of 4.

If the volume of the smaller prism is 64 cubic units,

then the volume of the larger prism = ___ un³.

• 4096

• 512

• 1024

• 256

Two similar solids have volumes of 640 cm³ and 1250 cm³.

If the larger solid has a surface area of 750 cm²,

then the smaller's SA = ___ cm².

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

• 64:121

• 8:11

• 120:242

• 512:1331

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

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

• Yes; 5

• Yes; 9:6

• Yes; 1/3

• No

Two similar solids have surface areas of 243 in² and 300 in².

If the larger solid has a volume of 500 in³,

then the smaller's volume = __ in³.

Two similar cubes have a scale factor of 2.

If the volume of the smaller cube is 27 cubic units,

what is the volume of the larger cube ?

• 64

• 100

• 216

• 54

Two similar cylinders have a scale factor of 3.

If the volume of the smaller cylinder is 100π cubic units,

what is the volume of the larger cylinder = ___ un³.

• 900π

• 2700π

• 200π

• 5400π