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Mathematical Models with Applications
Mathematical modeling in science and engineering
9. TX.MMA.6.B
9.1 Similar solids
Similar Solids in Geometry
Discover how similar solids share the same shape at different sizes, and how their scale factor controls both surface area and volume ratios.
What You'll Learn
Identify similar solids by checking that corresponding angles are equal and corresponding edges share one common ratio
Calculate the scale factor by dividing corresponding linear measurements of two similar solids
Apply the rule that the surface area ratio equals \( \dfrac{A_1}{A_2} = k^2 \).
Apply the rule that the volume ratio equals \( \dfrac{V_1}{V_2} = k^3 \).
Solve for an unknown edge, surface area, or volume using proportions built from the scale factor
Avoid the common mistake of using the linear scale factor directly for area or volume comparisons
This Unit Includes
8 Video lessons
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TX Curriculum Aligned