Name __________________________________________________________
Similarity Worksheet #6
Proportional Parts, Area, Volume
Use your new conjectures to solve each problem. All measurements are in centimeters.
Reminder: A midsegment of
a triangle is __________ the
length of the third side.
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14. The corresponding diagonals of two similar trapezoids are in the ratio 1:7. What is the ratio of their areas?
15. The ratio the perimeters of two similar parallelograms is 3:7. What is the ratio of their areas?
16. The ratio of the areas of two similar trapezoids is 1:9. What is the ratio of their altitudes?
17. The areas of two circles are in the ratio of 25:16. What is the ratio of their radii?
18. Two cubes have edges in the ratio of m/n. What is the ratio of their surface areas?
19. The Jones family paid $150 to a painting contractor to stain their 12 ft. by 15 ft. deck. Their neighbors, the Smiths,
have a similar deck 16 ft. by 20 ft. If the Smiths wish to “keep up with the Joneses,” what is a proportional price the
Smith family should expect to pay to have their deck stained by the contractor? (Tip: Draw & label a diagram.)
20. The corresponding edges of two similar triangular prisms are in the ratio of 5:3. What is the ratio of their volumes?
21. The volumes of two similar pentagonal prisms are in the ratio of 8:125. What is the ratio of their heights?
22. The ratio of the volumes of two similar circular cylinders is 27:64. What is the ratio of the diameters of their
similar bases?
23. The surface areas of two cubes are in the ratio of 49:81. What is the ratio of their volumes?
24. The ratio of the volume of two spheres is 1:125. What is the ratio of their surface areas?