Answer: The similarity ratio of the two cubes is 9 : 15.
Step-by-step explanation: We are to find the similarity ratio of a cube with volume 729 m³ to a cube with volume 3375 m³.
We know that if two solids are similar, then ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
Let, 'a' m and 'b' m be the lengths of two corresponding sides of the cubes with volumes 729 m³ and 3375 m³ respectively.
Then, we must have
\(729:3375=a^3:b^3\\\\\\\Rightarrow \dfrac{a^3}{b^3}=\dfrac{729}{3375}\\\\\\\Rightarrow \left(\dfrac{a}{b}\right)^3=\left(\dfrac{9}{15}\right)^3\\\\\\\Rightarrow \dfrac{a}{b}=\dfrac{9}{15}\\\\\\\Rightarrow a:b=9:15.\)
Thus, the similarity ratio of the two cubes is 9 : 15.
