Given Data:
Numbers to be rounded up to three significant figures:
- 34.216
- 0.04597
- 10.4107

Solution:

Step 1: Understanding significant figures:
Significant figures are the digits in a number that carry meaning in terms of its accuracy or precision. When rounding to a certain number of significant figures, we consider the digits that are significant and adjust the remaining digits accordingly.

Step 2: Identifying significant figures:
Let's identify the significant figures in each given number:

- 34.216: The digits 3, 4, 2, 1, and 6 are all significant.
- 0.04597: The digits 4, 5, 9, and 7 are all significant.
- 10.4107: The digits 1, 0, 4, 1, 0, and 7 are all significant.

Step 3: Rounding up to three significant figures:
To round up to three significant figures, we need to consider the digit at the fourth significant figure and adjust it based on the following rules:

- If the fourth significant figure is less than 5, we simply drop it and keep the first three significant figures unchanged.
- If the fourth significant figure is 5 or greater, we increase the third significant figure by 1 and drop the fourth significant figure.

Step 4: Rounding each number:
Let's apply the rounding rules to each given number:

- 34.216: The fourth significant figure is 6, which is 5 or greater. Therefore, we increase the third significant figure (2) by 1, resulting in 34.2.
- 0.04597: The fourth significant figure is 9, which is 5 or greater. Therefore, we increase the third significant figure (5) by 1, resulting in 0.0461.
- 10.4107: The fourth significant figure is 7, which is 5 or greater. Therefore, we increase the third significant figure (4) by 1, resulting in 10.4.

Step 5: Final set of rounded figures:
After rounding up to three significant figures, the set of figures obtained is:
- 34.2
- 0.0461
- 10.4

Final Answer:
The set of figures obtained after rounding up the given numbers to three significant figures is Option B) 34.2, 0.0461, 10.4.