Ratios of Surface Area and Volume of Similar 3D Figures

Calculate the composite surface area of the square pyramid on top of the square prism.

• 8160 cm²
• 2400 cm²
• 3456 cm²
• 2304 cm²

If two figures are similar, their area ratio is ...?

• the same

• squared

• cubed

• twice as much

If two figures are similar, their volume ratio is ...?

• the same

• squared

• cubed

• three times as much

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

If all the edges of a prism are multiplied by 5, then the volume of the prism will be multiplied by ___.

• 5
• 25
• 50
• 125

Tags

CCSS.7.G.B.6

If the side lengths are tripled, then which of the following statements about its surface area will be true?

• The new surface area will be 3 times larger

• The new surface area will be 9 times larger

• The new surface area will be 10 times larger

• The new surface area will be 27 times larger

Tags

CCSS.6.G.A.4

If the side lengths are tripled, then which of the following statements about its volume will be true?

• The new volume will be 3 times larger

• The new volume will be 9 times larger

• The new volume will be 10 times larger

• The new volume will be 27 times larger

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

What is the scale factor of the side lengths of the figure on the left to the figure on the right.

• 3/1

• 3240/120

• 27/1

• 9/1

Two spheres have a scale factor ratio of 1:3.  The smaller sphere has a surface area of 16 ft²_.  Find the surface area of the larger sphere.

• 48 ft²
• 144 ft²
• 432 ft²
• 32 ft²

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The volume of a prism is 1000 cubic centimeters. A similar prism has a volume of 27 cubic centimeters. What is the ratio of their surface areas?

• 100:9

• 10:3

• 500:13.5

• 100:2.7

Tags

CCSS.7.G.B.6