http://www.ck12.org Chapter 11. Surface Area and Volume
First, we need to take the square root of the area ratio to find the scale factor,
√
16
25
=^45. Now we can set up aproportion to findh.
4
5
=
24
h
4 h= 120
h= 30Example C
Two spheres have radii in a ratio of 3:4. What is the ratio of their volumes?
If we cube 3 and 4, we will have the ratio of the volumes. Therefore, 3^3 : 4^3 or 27:64 is the ratio of the volumes.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52645CK-12 Foundation: Chapter11AreaandVolumeofSimilarSolidsB
Concept Problem Revisited
The coffee mugs are similar because the heights and radii are in a ratio of 2:3, which is also their scale factor. The
volume of Dad’s mug is 54πin^3 and Mom’s mug is 16πin^3. The ratio of the volumes is 54π: 16π, which reduces to
8:27.
Vocabulary
Two solids aresimilarif they are the same type of solid and their corresponding radii, heights, base lengths, widths,
etc. are proportional.
Guided Practice
- Determine if the two triangular pyramids are similar.