Similar Solids Worksheet
Explore the properties of similar solids, including their surface area and volume ratios, with this Grade 10 math worksheet.
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Similar Solids: Surface Area and Volume Ratios
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. If two solids are similar and the ratio of their corresponding linear dimensions is 3:5, what is the ratio of their surface areas?
3:5
9:25
27:125
6:10
2. The volumes of two similar cones are in the ratio 8:27. What is the ratio of their heights?
2:3
4:9
8:27
16:81
3. If the ratio of the surface areas of two similar solids is a²:b², then the ratio of their corresponding linear dimensions is .
4. If two similar solids have a linear ratio of m:n, their volumes will be in the ratio .
5. Two similar cylinders have radii of 4 cm and 6 cm respectively. If the surface area of the smaller cylinder is 48π cm², what is the surface area of the larger cylinder?
6. A spherical balloon is inflated such that its diameter doubles. How many times greater is its new volume compared to its original volume?
7. If two solids are similar, their corresponding angles are congruent.
True
False
8. The ratio of the volumes of two similar solids is equal to the cube of the ratio of their corresponding linear dimensions.
True
False
9. A model of a building is constructed with a scale of 1:50. If the actual building has a volume of 250,000 m³, what is the volume of the model in cubic meters?