Similar Solids Worksheet

Explore the properties of similar solids, including their scale factors, surface areas, and volumes, with these geometry problems.

Grade 9 Math GeometrySimilar Solids

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Multiple ChoiceFill in the BlanksShort AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSG.MG.A.1CCSS.MATH.CONTENT.HSG.GMD.A.3

Topics

MathGeometrySimilar SolidsGrade 9

7 sections · Free to use · Printable

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Similar Solids: Scale Factors and Proportions

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Read each question carefully and provide the best answer. Show all your work for short answer questions.

1. If two solids are similar with a scale factor of 3:5, what is the ratio of their surface areas?

3:5

9:25

27:125

5:3

2. The volumes of two similar cones are in the ratio 8:27. What is the ratio of their heights?

8:27

64:729

2:3

4:9

3. If the ratio of the corresponding linear dimensions of two similar solids is a:b, then the ratio of their surface areas is and the ratio of their volumes is .

4. Two cubes are similar. The smaller cube has a side length of 4 cm and the larger cube has a side length of 8 cm. The scale factor from the smaller to the larger cube is .

5. A small sphere has a radius of 3 cm. A larger sphere is similar to the small sphere and has a radius of 9 cm. Calculate the ratio of their volumes.

6. Two similar cylinders have heights of 6 inches and 18 inches. If the surface area of the smaller cylinder is 50 square inches, what is the surface area of the larger cylinder?

7. The two rectangular prisms below are similar. Find the volume of the larger prism if the volume of the smaller prism is 60 cubic units.

8. All cubes are similar to each other.

True

False

9. If the ratio of the surface areas of two similar solids is 4:9, then the ratio of their volumes is 2:3.

True

False