Final answer:
The surface area of solid x is approximately 4.75 cm².
Step-by-step explanation:
To find the surface area of solid x, we need to use the fact that the two solids x and y are similar. Since the ratio of their volumes is given as 64:125, we can say that the ratio of their side lengths is the cube root of that ratio. Let's call the side length of solid x 'a'. Therefore, the side length of solid y would be (125/64)^(1/3) * a. Now that we know the side lengths of the two solids, we can determine their surface areas by using the formulas for surface area of a cube. The surface area of solid y is given as 80 cm, so we can set up the equation 6 * [(125/64)^(1/3) * a]^2 = 80. Solving for 'a', we find that a ≈ 0.867 cm. Finally, we can find the surface area of solid x by substituting this value into the formula for surface area of a cube: 6 * a^2. Plugging in the value of 'a', the surface area of solid x is approximately 4.75 cm².