一炉铁水凝成铁块，其体积缩小了 1/34，那么这个铁块又熔化成铁水(不计损耗)，其体积增加了几分之几？---**Extracted Content:** **Question Stem:** Exploration 4: 一炉铁水凝成铁块，其体积缩小了 1/34，那么这个铁块又熔化成铁水(不计损耗)，其体积增加了几分之几？ **Translation of Question Stem:** Exploration 4: A furnace of molten iron solidifies into an iron block, and its volume shrinks by 1/34. If this iron block is then melted back into molten iron (disregarding loss), by what fraction does its volume increase? **Other Relevant Text (Handwritten Calculations/Solution Hint):** The image contains handwritten calculations that appear to be a solution or a derivation for the question. * **Line 1 of Calculation:** `1` `--- = 33` `34` *(Note: This line, as directly transcribed, is mathematically incorrect. It likely represents a shortcut or a conceptual derivation. A common pattern is that if a quantity decreases by 1/N, it needs to increase by 1/(N-1) of the new quantity to return to the original. In this case, N=34, so 1/(34-1) = 1/33. The "33" on the right side might indicate the result of this calculation, while the fraction on the left might be an incomplete representation of the intended formula or concept.)* * **Line 2 of Calculation:** `(34/33 - 1) = 1/33` *(Note: This calculation correctly determines the fractional increase. If the original volume is V, and it shrinks by 1/34, the new volume is V * (1 - 1/34) = V * (33/34). To find the original volume from the new volume, you multiply the new volume by (34/33). The increase relative to the new volume is (V * (34/33) - V * (33/34)) / (V * (33/34)), or more simply, (Original Volume / New Volume) - 1, which is (34/33) - 1 = 1/33.)*