Lesson Worksheet: Similarity of Solids Mathematics • 8th Grade
In this worksheet, we will practice identifying similar solids and using similarity to find their dimensions, areas, and volumes.
Q2:
The figure shows two cubes. If the area of the smaller one is 143, and the sides are in the ratio , what is the surface area of the larger cube?
Q7:
A pair of regular triangular pyramids are similar. Pyramid A has a base side of 17 inches and a slant height of 20 inches, whereas pyramid B has a base side of inches and a slant height of 42 inches. Determine the value of .
Q8:
A pair of rectangular prisms are similar. Prism is 104 by 32 by 24 inches, while prism is 26 by 8 by inches. Find.
Q9:
A pair of cylinders are similar. Cylinder A has a base radius of 29 inches and a length of 6 inches, and cylinder B has a base radius of inches and a length of 18 inches. Determine the value of .
Q10:
The surface areas of two similar solids are 64 square yards and 361 square yards. Find the ratio of their linear measures.
- A
- B
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- E
Q11:
The given pair of rectangular prisms are similar. If the surface area of the smaller rectangular prism is 310 yd2, determine the surface area of the larger one.
Q12:
A cone has a volume of 11,756 cubic centimeters. Suppose that its dimensions were reduced as the figure shows, find the volume of the resulting cone.
Q13:
What is the scale factor of two similar cylinders whose volumes are 1,331 and 1,728 cubic meters?
- A
- B
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- D
- E
Q16:
Two similar cones have radii of 5 millimeters and 10 millimeters. What is the ratio of the surface area of the small cone to the surface area of the large one?
- A
- B
- C
- D4
- E2
Q17:
Two similar cones have surface areas of 768 and 363. What is the ratio of the height of the larger cone to that of the smaller one?
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- B
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- D
- E