1. Problem 49: Find the ratio of the total surface area of three small cubes with side lengths 3 cm, 4 cm, and 5 cm to the surface area of a large cube made by combining their volumes. 2. Calculate the volume of each small cube: $$V_1 = 3^3 = 27, \quad V_2 = 4^3 = 64, \quad V_3 = 5^3 = 125$$ 3. Total volume of the large cube: $$V = 27 + 64 + 125 = 216$$ 4. Side length of the large cube: $$s = \sqrt[3]{216} = 6$$ 5. Calculate total surface area of small cubes: $$SA_1 = 6 \times 3^2 = 54, \quad SA_2 = 6 \times 4^2 = 96, \quad SA_3 = 6 \times 5^2 = 150$$ 6. Total surface area of small cubes: $$SA_{small} = 54 + 96 + 150 = 300$$ 7. Surface area of the large cube: $$SA_{large} = 6 \times 6^2 = 216$$ 8. Ratio of total surface area of small cubes to large cube: $$\frac{SA_{small}}{SA_{large}} = \frac{300}{216} = \frac{25}{18}$$ --- 9. Problem 50: Find the distance between points $P(2,1)$ and $Q(4,3)$. 10. Use the distance formula: $$PQ = \sqrt{(4-2)^2 + (3-1)^2} = \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$$ Final answers: - Problem 49 ratio: 25 : 18 - Problem 50 distance: $2\sqrt{2}$ units