http://www.ck12.org Chapter 11. Surface Area and Volume
11.9 Area and Volume of Similar Solids
Here you’ll learn how to use the ratios between similar solids to solve problems.
What if you had to compare your parents’ cylindrical coffee mugs with different dimensions, pictured below? Are
the mugs similar? (You may ignore the handles.) If the mugs are similar, find the volume of each, the scale factor
and the ratio of the volumes. After completing this Concept, you’ll be able to solve problems like these.
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MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52644CK-12 Foundation: Chapter11AreaanVolumeofSimilarSolidsA
Learn more about similarity and volume ratios by watching the video at this link.
Guidance
Two solids aresimilarif and only if they are the same type of solid and their corresponding linear measures (radii,
heights, base lengths, etc.) are proportional.
Surface Area
Recall that when two shapes are similar, the ratio of the area is a square of the scale factor.
For example, the two rectangles above are similar because their sides are in a ratio of 5:8. The area of the larger
rectangle is 8( 16 ) = 128 units^2 and the area of the smaller rectangle is 5( 10 ) = 50 units^2. If we compare the areas
in a ratio, it is 50 : 128=25 : 64= 52 = 82.