1. **State the problem:** We have two similar right rectangular prisms X and Y. - Surface area of X: $58$ cm² - Surface area of Y: $1450$ cm² - Volume of Y: $1250$ cm³ We need to find the sum of the volumes of prisms X and Y. 2. **Recall formulas and properties:** - For similar solids, the ratio of surface areas is the square of the scale factor: $$\frac{SA_X}{SA_Y} = k^2$$ - The ratio of volumes is the cube of the scale factor: $$\frac{V_X}{V_Y} = k^3$$ 3. **Find the scale factor $k$:** $$k^2 = \frac{SA_X}{SA_Y} = \frac{58}{1450} = \frac{58 \div 58}{1450 \div 58} = \frac{1}{25}$$ 4. **Calculate $k$:** $$k = \sqrt{\frac{1}{25}} = \frac{1}{5}$$ 5. **Find volume of X using volume ratio:** $$\frac{V_X}{1250} = \left(\frac{1}{5}\right)^3 = \frac{1}{125}$$ $$V_X = 1250 \times \frac{1}{125} = 10$$ 6. **Find the sum of volumes:** $$V_X + V_Y = 10 + 1250 = 1260$$ **Final answer:** The sum of the volumes is $1260$ cm³.