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Sagot :
the ratio of the surface areas of similar solids is equal to the square of their scale factor and that the ratio of their volumes is equal to the cube of their scale factor.
If two solids are similar with a scale factor of a/b, then the surface areas are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^2[/tex].
If two solids are similar with a scale factor of a/b, then the volumes are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^3[/tex].
What are the area and volume of similar solids?
Two shapes are similar if all their corresponding angles are congruent and their corresponding sides are proportional.
Two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.
When two shapes are similar in two dimensions, the ratio of their areas is the square of the scale factor.
A comparable relationship holds in three dimensions as well.
Surface Area Ratio: If two solids are similar with a scale factor of a/b, then the surface areas are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^2[/tex].
Volumes of Similar Solids; Just like surface area, volumes of similar solids have a relationship that is related to the scale factor.
Volume Ratio: If two solids are similar with a scale factor of a/b, then the volumes are in a ratio of [tex]\rm \left (\dfrac{a}{b } \right )^3[/tex].
Learn more about the area here;
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