The first thing we must do for this case is find the scale factor.
We have then:
[tex] k^2=\frac{1158}{340} [/tex]
Rewriting we have:
[tex] k^2=3.4 [/tex]
[tex] k=1.8 [/tex]
Then, we look for the value of the smallest solid volume.
For this, we have the following relationship.
[tex] V1=k^3V2 [/tex]
Where,
V1: volume of the largest solid
V2: volume of the smallest solid
k: scale factor
Clearing V2 we have:
[tex] V2 = \frac{V1}{k^3} [/tex]
Substituting values we have:
[tex] V2 = \frac{1712}{1.8^3} [/tex]
[tex] V2=293.6 [/tex]
Answer:
the volume of the smaller solid is 293.6 yd^3
