Final answer:
The cube root of 217.1 is only slightly larger than the cube root of 216, which is 6. The increase wouldn't accurately match any of the provided options (0.1, 0.5, 0.9, or 1.3), but it would be less than 0.1 since cube roots increase slowly.
Step-by-step explanation:
The student asked, 'How much larger is the cube root of 217.1 compared to the cube root of 216?' Since we know that the cube root of 216 is equal to 6, we need to find out by how much the value increases when the cube root of 217.1 is taken. To estimate the cube root of 217.1, we can use the fact that it is very close to the cube root of 216, which we know is 6. Because cube roots tend to increase slowly as the numbers get larger, especially within such a small range, the cube root of 217.1 will be slightly more than 6, but the increase is unlikely to be as much as 0.1.
Therefore, without detailed calculations, we can infer that none of the supplied options, a) 0.1, b) 0.5, c) 0.9, or d) 1.3, would accurately represent the increase in the cube root from 216 to 217.1. To find out how much larger the cube root of 217.1 is compared to the cube root of 216, we can subtract the two values. The cube root of 216 is 6, and the cube root of 217.1 is approximately 6.0218. Therefore, the cube root of 217.1 is approximately 0.0218 larger than the cube root of 216.