SAT Question 73e1b793: Area and Volume answer and explanation with Desmos solution

It’s given that right rectangular prism P is similar to right rectangular prism Q. Therefore, there is a positive constant $k$ such that the length of each edge of prism P is $k$ times the length of the corresponding edge of prism Q and the volume of prism P is $k^3$ times the volume of prism Q. It’s given that the volume of prism P is $972{\text{cm}}^3$ and the volume of prism Q is $36{\text{cm}}^3$. It follows that $972=36k^3$. Dividing both sides of this equation by $36$ yields $\frac{972}{36}=k^3$, or $k^3=27$. Taking the cube root of both sides of this equation yields $k=3$. It follows that the length of each edge of prism P is $3$ times the length of the corresponding edge of prism Q. It’s given that one edge of prism P has a length of $12$ cm. It follows that $12$ cm is $3$ times the length of the corresponding edge of prism Q. Thus, the length, in cm, of the edge of prism Q corresponding to the edge of prism P with a length of $12$ cm is $\frac{12}{3}$, or $4$.