G14a Similar Solids

Two spheres have a similarity ratio of 1:3.  The smaller sphere has a surface area of 16 ft²_.  What is the surface area of the larger sphere.

• 48 ft²
• 144 ft²
• 432 ft²
• 32 ft²

What is the ratio of the volumes from larger to smaller. (HINT* Find the ratio of the side lengths first)

• 5/4
• 125/64
• 25/16
• 10/8

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Given two similar prisms with a scale factor of 3:4, which of the following is NOT true?

• Ratio of their areas is 9:16
• Ratio of their perimeters is 3:4
• Ratio of their volumes is 27:64
• Ratio of their corresponding angles is 3:4

Tags

CCSS.HSG.SRT.A.1

CCSS.HSG.SRT.A.2

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.SRT.A.2

Find the ratio of the surface areas from larger to smaller.

• 5/4
• 200/160
• 25/16
• 10/8

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

Pyramid X is similar to pyramid Y. The surface area of pyramid X is 135 cm² and the surface area of pyramid Y is 240 cm². If the volume of pyramid X is 189 cm³, then what is the volume of pyramid Y?

• 448 cm³

• 1061.9 cm³

• 252 cm³

• 336 cm³

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.SRT.A.2

The ratio of the areas of two similar rectangles is 1:4. What is the ratio of the corresponding sides?

• 1:6
• 1:8
• 1:2
• 1:4

Tags

CCSS.HSG.SRT.A.2

The ratio of the volumes of two spheres is 64:27. What is the ratio of the lengths of the radii of these two spheres?

• 2:1
• 3:4
• 4:3
• 4:9

Tags

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.SRT.A.2

The volume of Pyramid A is $704\ cm^3$  and the volume of Pyramid B is  $297\ cm^3$  . If the pyramids are similar and the surface area of Pyramid B is  $153\ cm^2$ , find the surface area of Pyramid A.

•  $204\ cm^2$  

•  $362.67\ cm^2$  

•  $272\ cm^2$  

•  $408\ cm^2$  

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.SRT.A.2