Answer:[tex]27:125[/tex]
Step-by-step explanation:
Given
Ratio of corresponding dimensions is in the ratio of [tex]3:5[/tex]
If the two pyramids are similar then the ratio of their volumes is proportional to the cube of their side ratio
i.e.
[tex]\Rightarrow \dfrac{V_1}{V_2}=(\dfrac{l_1}{l_2})^3[/tex]
[tex]\Rightarrow \dfrac{V_1}{V_2}=(\dfrac{3}{5})^3[/tex]
[tex]\Rightarrow \dfrac{V_1}{V_2}=\dfrac{27}{125}[/tex]
Thus the ratio of their volumes is [tex]27:125[/tex]