1. **State the problem:** We have two similar right rectangular prisms, X and Y. Surface area of X is 46 cm², surface area of Y is 1656 cm². Volume of Y is 4320 cm³. We need to find the sum of the volumes of X and Y. 2. **Recall formulas and properties:** For similar solids, the ratio of surface areas is the square of the scale factor $k$: $$\frac{S_Y}{S_X} = k^2$$ The ratio of volumes is the cube of the scale factor: $$\frac{V_Y}{V_X} = k^3$$ 3. **Calculate the scale factor $k$:** $$k^2 = \frac{S_Y}{S_X} = \frac{1656}{46} = 36$$ So, $$k = \sqrt{36} = 6$$ 4. **Find volume of X:** Using volume ratio, $$\frac{V_Y}{V_X} = k^3 = 6^3 = 216$$ So, $$V_X = \frac{V_Y}{216} = \frac{4320}{216} = 20$$ 5. **Find sum of volumes:** $$V_X + V_Y = 20 + 4320 = 4340$$ **Final answer:** The sum of the volumes of prisms X and Y is **4340 cm³**.