1. **Problem Statement:** Find the missing volume $V$ of Solid #2 given the surface areas and volume of Solid #1 and the surface area of Solid #2. Given: - Solid #1: $SA_1 = 1088$ km², $V_1 = 13312$ km³ - Solid #2: $SA_2 = 425$ km², $V_2 = ?$ 2. **Formula and Rules:** For similar solids, the ratio of surface areas is the square of the scale factor $k$, and the ratio of volumes is the cube of the scale factor $k$: $$\frac{SA_1}{SA_2} = k^2 \quad \text{and} \quad \frac{V_1}{V_2} = k^3$$ We can find $k$ from the surface areas and then use it to find $V_2$. 3. **Calculate the scale factor $k$:** $$k^2 = \frac{SA_1}{SA_2} = \frac{1088}{425}$$ Calculate $k$: $$k = \sqrt{\frac{1088}{425}} = \sqrt{2.56} = 1.6$$ 4. **Use $k$ to find $V_2$:** $$\frac{V_1}{V_2} = k^3 \Rightarrow V_2 = \frac{V_1}{k^3}$$ Calculate $k^3$: $$k^3 = (1.6)^3 = 4.096$$ Calculate $V_2$: $$V_2 = \frac{13312}{4.096}$$ Show intermediate cancellation: $$V_2 = \frac{\cancel{13312}}{\cancel{4.096}} = 3248$$ 5. **Final answer:** The volume of Solid #2 is: $$\boxed{3248 \text{ km}^3}$$