Final answer:
To calculate the volume of a cube given its curved surface area of 256 m², divide by 6 to find the area of one side, take the square root to find the side length, and then cube that length to find the volume. However, the calculated volume does not match any of the provided options, hinting at a possible mistake in the initial values or a trick question.
Step-by-step explanation:
To find the volume of a cube when you know the curved surface area, you can start by finding the length of one side of the cube. Since a cube has six equal sides and the question gives us the total curved surface area, we first divide the total surface area by 6 to find the area of one side. The question states that The curved surface area of a cube is 256 m². So, the area of one side would be 256 m² divided by 6, which is approximately 42.67 m². Next, since the area of one side of a cube is equal to the square of its side length (s²), we can find the side length (s) by taking the square root of the area of one side. In this case, the square root of approximately 42.67 m² is approximately 6.53 m, which is the length of one side of the cube. Finally, the volume of a cube is found by raising the side length to the third power (s³). So, the volume of the cube would be approximately 6.53 m raised to the third power, which gives us approximately 279.5 m³. Since none of the options exactly match this figure, there might have been a mistake in the starting values, or this might be a trick question. It's essential to double-check the calculation and the question prompt to ensure accuracy.