11.9. Area and Volume of Similar Solids http://www.ck12.org
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.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter11AreaanVolumeofSimilarSolidsA
MEDIA
Click image to the left for more content.Brightstorm:Similarity and Volume Ratios
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.
Surface Area Ratio:If two solids are similar with a scale factor ofab, then the surface areas are in a ratio of
(a
b) 2
.
Volume
Let’s look at what we know about similar solids so far.