Answer: [tex]132cm^{3}[/tex]
Explanation:
The volume [tex]V[/tex] of a solid is given by the multiplication of its three dimensions:
[tex]V=(height)(widgth)(length)[/tex]
In this case we have two similar solids with volumes [tex]V_{1}=88cm^{3}[/tex] and [tex]V_{2}[/tex], and we only have information about the height of each solid [tex]h_{1}=6cm[/tex] and [tex]h_{2}=9cm[/tex].
Now, there is a theorem for similar solids, which establishes the ratio of their volume is [tex]\frac{V_{1}}{V_{2}}[/tex] and the ratio of one of their corresponding sides (the height in this case) is [tex]\frac{h_{1}}{h_{2}}[/tex].
Knowing this, we can write the following relation:
[tex]\frac{V_{1}}{V_{2}}=\frac{h_{1}}{h_{2}}[/tex]
Substituting the known values:
[tex]\frac{88cm^{3}}{V_{2}}=\frac{6cm}{9cm}[/tex]
Fially finding [tex]V_{2}[/tex]:
[tex]V_{2}=132cm^{3}[/tex]
