11.7. Exploring Similar Solids http://www.ck12.org
√ (^3) 125 :√ (^38) =5 : 2
Example 9:Two similar right triangle prisms are below. If the ratio of the volumes is 343:125, find the missing
sides in both figures.
Solution:If the ratio of the volumes is 343:125, then the scale factor is 7:5, the cubed root of each. With the scale
factor, we can now set up several proportions.
7
5
=
7
y7
5
=
x
107
5
=
35
w72 +x^2 =z^27
5
=
z
v
y= 5 x= 14 w= 25 72 + 142 =z^2z=√
245 = 7
√
5
7
5
=
7
√
5
v→v= 5√
5
Example 10:The ratio of the surface areas of two similar cylinders is 16:81. If the volume of the smaller cylinder
is 96πin^3 , what is the volume of the larger cylinder?
Solution:First we need to find the scale factor from the ratio of the surface areas. If we take the square root of both
numbers, we have that the ratio is 4:9. Now, we need cube this to find the ratio of the volumes, 4^3 : 9^3 =64 : 729.
At this point we can set up a proportion to solve for the volume of the larger cylinder.
64
729
=
96 π
V
64 V= 69984 π
V= 1093. 5 πin^3Know What? RevisitedThe 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
54 π: 16π, which reduces to 8:27.
Review Questions
Determine if each pair of right solids are similar.Explainyour reasoning.