OG详解-OG9 数学1 Q27

The correct answer is 1,260. 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 k² times the surface area of prism X and the volume of prism Y is k³  times the volume of prism X. It’s given that the surface area of prism Y is 1,450 cm², and the surface area of prism X is 58 cm2, which implies that 1,450 = 58k². Dividing both sides of this equation by 58 yields 1,45058​​= k², or k² = 25. Since k is a positive constant, k = 5. It’s given that the volume of prism Y is 1,250 cm³. Therefore, the volume of prism X is equal to cm³, which is equivalent to cm³ , or 10 cm³. Thus, the sum of the volumes, in cm³, of the two prisms is 1,250+10, or 1,260.