Answer:
The volume of the smaller solid is [tex]339\ yd^{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z----> the scale factor
x----> surface area of the larger solid
y----> surface area of the smaller solid
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=361\ yd^{2}[/tex]
[tex]y=121\ yd^{2}[/tex]
substitute
[tex]z^{2}=\frac{361}{121}[/tex]
[tex]z=\frac{19}{11}[/tex]
step 2
Find the volume of the smaller solid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z----> the scale factor
x----> volume of the larger solid
y----> volume of the smaller solid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{19}{11}[/tex]
[tex]x=1,747\ yd^{3}[/tex]
substitute
[tex](\frac{19}{11})^{3}=\frac{1,747}{y}\\ \\(\frac{6,859}{1,331})=\frac{1,747}{y} \\ \\y=1,331*1,747/6,859\\ \\y=339\ yd^{3}[/tex]
