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Similar Solids Worksheets

Identify similar solid figures from labelled lengths and sketch scaled copies, with exact scale factors and example solutions.

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Use the labelled lengths, not the apparent drawing size. Explain similarity or sketch the requested scaled solid.

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A4

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Paper sizes and printing help · More geometry activities

One scale factor must fit every length

Use the printed corresponding dimensions instead of judging the apparent drawing size. Sketch tasks state a positive scale factor and the key labels every resulting dimension.

Learning objective

What this activity builds

Recognize and construct solids whose corresponding lengths share one scale factor.

Worked example

A cylinder has radius 3 and height 5. What are these lengths after enlargement by a factor of 2?

Radius 6 and height 10.

Every corresponding length is multiplied by the same factor. Doubling only the radius would change the shape.

Teaching notes

Make the practice count

  • Match corresponding dimensions before finding ratios.
  • A scaled sketch may be rotated without changing similarity.
  • Keep exact fractional lengths when the scale factor is a fraction.

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Math SheetNameScoreTeacherDateSimilar SolidsDecide whether each pair is similar or sketch the stated scaled solid. Compare every labelled corresponding length. Rectangular prisms are right, cylinders andcones are right circular solids, and each square-pyramid apex is directly above the base center. Diagrams are not to scale.1.Sketch a cone similar to the pictured solid with scale factor 3/2. Label every corresponding dimension. Scale factor: 3/2.radius = 54perpendicular height = 72Scaled sketch2.Are the two pictured solids similar? Justify using every labelled pair of corresponding lengths.length = 48width = 36height = 24length = 144width = 108height = 72Similar?Diagrams are not to scale.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateSimilar SolidsDecide whether each pair is similar or sketch the stated scaled solid. Compare every labelled corresponding length. Rectangular prisms are right, cylinders andcones are right circular solids, and each square-pyramid apex is directly above the base center. Diagrams are not to scale.3.Are the two pictured solids similar? Justify using every labelled pair of corresponding lengths.base side = 24perpendicular height = 18base side = 16perpendicular height = 13Similar?4.Sketch a cylinder similar to the pictured solid with scale factor 2/3. Label every corresponding dimension. Scale factor: 2/3.radius = 12height = 30Scaled sketchDiagrams are not to scale.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateSimilar SolidsDecide whether each pair is similar or sketch the stated scaled solid. Compare every labelled corresponding length. Rectangular prisms are right, cylinders andcones are right circular solids, and each square-pyramid apex is directly above the base center. Diagrams are not to scale.5.Sketch a cone similar to the pictured solid with scale factor 2/3. Label every corresponding dimension. Scale factor: 2/3.radius = 36perpendicular height = 48Scaled sketch6.Are the two pictured solids similar? Justify using every labelled pair of corresponding lengths.radius = 24height = 60radius = 16height = 40Similar?Diagrams are not to scale.math-sheet.comPage 3 of 3

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