Final answer:
To find the surface area of the larger solid, we can use the concept of similarity. Since the volumes of the two solids are in the ratio 728:125, we can assume that the corresponding sides are also in the same ratio. Using this information, we can calculate the side length and then the surface area of the larger solid.
Step-by-step explanation:
To find the surface area of the larger solid, we can use the concept of similarity. Since the volumes of the two solids are in the ratio 728:125, we can assume that the corresponding sides are also in the same ratio. Let's assume that the ratio of the sides is x. So, the ratio of the volumes is x³. We know that the surface area of the smaller solid is 74.33 inches². So, we can set up the equation 6s² = 74.33, where s is the side length of the smaller solid. Solving this equation, we find that s ≈ 4.23 inches.
Since the ratio of the sides is x, we can calculate the side length of the larger solid by multiplying the side length of the smaller solid by x. So, the side length of the larger solid is 4.23x inches. Now, we can calculate the surface area of the larger solid using the formula 6s², where s is the side length. Plugging in the value of s, we get 6(4.23x)².
To find the value of x, we can set up the equation (4.23x)³/125 = 728/125. Solving this equation, we find that x ≈ 3. So, the side length of the larger solid is approximately 4.23 × 3 = 12.69 inches. Plugging this value into the surface area formula, we get 6(12.69)². Calculating this, the surface area of the larger solid is approximately 128.82 inches².