SAT Question 167aff9e: Area and Volume answer and explanation with Desmos solution

Since it's given that prisms X and Y are similar, all the linear measurements of prism Y are $k$ times the respective linear measurements of prism X, where $k$ is a positive constant. Therefore, the surface area of prism Y is $k^2$ times the surface area of prism X and the volume of prism Y is $k^3$ times the volume of prism X. It's given that the surface area of prism Y is $1,450{\text{cm}}^2$, and the surface area of prism X is $58{\text{cm}}^2$, which implies that $1,450=58k^2$. Dividing both sides of this equation by $58$ yields $\frac{1,450}{58}=k^2$, or $k^2=25$. Since $k$ is a positive constant, $k=5$. It's given that the volume of prism Y is $1,250{\text{cm}}^3$. Therefore, the volume of prism X is equal to $\frac{1,250}{k^3}{\text{cm}}^3$, which is equivalent to $\frac{1,250}{5^3}{\text{cm}}^3$, or $10{\text{cm}}^3$. Thus, the sum of the volumes, in ${\text{cm}}^3$, of the two prisms is $1,250+10$, or $1,260$.