Similarity with Area and Volume

Two tents are in the shape of hemispheres, with circular floors. The ratio of their floor area is 9:12.25. If the diameter of the smaller tent is 6 teet, what is the volume of the larger tent? round to the nearest tenth.

(a)  

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

The ratio of the volume of two spheres is 8:27. What is the ratio of their radii?

• 2:3

• 4:9

• 3:4

• 64:729

Two rectangular prism are similar. The height of the first prism is 6 yards and the height of the other prism is 9 feet. If the volume of the first prism is 810 cubic yards, what is the volume of the other prism?( Type numerical part only)

(a)  

Find the volume of this square pyramid.

• 214.8 m³

• 586.7 m³

• 1818.2 m³

• not enough information

Tags

CCSS.HSG.GMD.A.3

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

The two figures are similar. Find the scale factor of the figure on the left to the figure on the right. Then find the ratio of surface areas and the ratio of volumes.

• 3:4, 27:8, 9:128

• 3:1, 9:1, 27:1

• 3:1, 9:1, 81:1

• 3:1, 6:1, 9:1

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

• Yes; 3

• Yes; 3/10

• Yes; 3/5

• No

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2