请制作一个解题视频，说明解题思路---Here is the extracted content from the image: **Question Stem:** 1. 某兴趣小组要测量一金属块的密度，设计了如下方案：将装有适量细沙的薄壁圆筒，缓慢竖直放入盛有适量水的、水平放置的长方体透明薄壁容器中，待圆筒静止后，在圆筒上对应水面的位置标记一点A，并在长方体容器上标出此时的水位线MN (如图甲所示)；然后将待测金属块用细线悬挂在圆筒下方，缓慢竖直放入水中，圆筒静止后 (金属块不接触容器底部)，在长方体容器上标出此时的水位线PQ (如图乙所示)；再向长方体容器中缓慢注水至圆筒上的A点与MN在同一水平面上 (如图丙所示)。测出PQ与此时水面的距离为h₁, 与MN的距离为h₂。若圆筒的底面积为S，长方体容器的底面积为4S，A点到圆筒底部的竖直距离为h，不计细线的质量和体积，已知ρ_水和g。 **Sub-questions:** (1) 求图甲中圆筒和细沙总重力G的大小 (用题中给出的物理量符号表示)； (2) 求金属块的体积V (用题中给出的物理量符号表示)； (3) 若h₁ = 0.07m, h₂ = 0.03m, ρ_水 = 1.0 × 10³ kg/m³ 求金属块的密度ρ。 **Mathematical/Physical Symbols and Given Values:** * Round cylinder base area: S * Rectangular container base area: 4S * Vertical distance from point A to the cylinder bottom (in Fig. 甲): h * Distance from PQ to the current water surface (in Fig. 丙): h₁ * Distance from MN to the current water surface (in Fig. 丙): h₂ *(Note: Based on diagram 丙's labels, h₁ appears to be the vertical distance between line MN and line PQ, and h₂ appears to be the vertical distance from point A (which is at MN) to the bottom of the submerged part of the cylinder. This is a common interpretation for solvable problems given the visual context, despite potential ambiguity in the textual description "测出PQ与此时水面的距离为h₁, 与MN的距离为h₂" where "此时水面" is PQ.)* * Density of water: ρ_水 * Acceleration due to gravity: g * Specific values for sub-question (3): h₁ = 0.07m, h₂ = 0.03m, ρ_水 = 1.0 × 10³ kg/m³ **Chart/Diagram Descriptions:** The image displays three schematic diagrams (labeled 甲, 乙, 丙) illustrating an experimental procedure to measure the density of a metal block. All diagrams show a thin-walled cylindrical tube containing fine sand, floating vertically in a larger rectangular transparent container filled with water, placed on a horizontal surface. * **Diagram 甲 (Jia):** * **Type:** Schematic diagram of the initial setup for measuring the weight of the floating cylinder. * **Main Elements:** * A cylindrical tube, containing "细沙" (fine sand), is floating upright in a rectangular container filled with "水" (water). * A horizontal line labeled "MN" is marked on the rectangular container, indicating the initial water level. * A point "A" is marked on the side of the cylindrical tube, aligned horizontally with the water level MN. * A vertical double-headed arrow labeled "h" indicates the vertical distance from point A down to the bottom base of the submerged part of the cylinder. * The base of the cylinder is labeled "S". * The setup rests on a horizontally hatched surface representing the ground. * **Diagram 乙 (Yi):** * **Type:** Schematic diagram of the setup with the metal block suspended. * **Main Elements:** * The cylindrical tube with sand is still floating in the rectangular container. * A "金属块" (metal block) is suspended by a thin line from the bottom of the cylindrical tube. The metal block is fully submerged in the water but does not touch the bottom of the rectangular container. * Due to the added weight of the metal block, the cylindrical tube has sunk deeper, and the water level in the rectangular container has risen. * A new horizontal line labeled "PQ" is marked on the rectangular container, indicating this new water level. * The original water level line "MN" is visible below PQ. * Point A on the cylinder is now above the water level PQ. * **Diagram 丙 (Bing):** * **Type:** Schematic diagram of the setup after adding water to adjust the cylinder's position. * **Main Elements:** * The cylindrical tube with sand and the suspended metal block are still in the rectangular container. * Additional water has been added to the rectangular container, causing the water level to rise further. * The cylindrical tube has sunk deeper such that point "A" on the cylinder is now horizontally aligned with the original water level line "MN". * The water level in the rectangular container is at the line "PQ". * A vertical double-headed arrow labeled "h₁" indicates the vertical distance between the line MN and the line PQ (i.e., the vertical rise of the water level from MN to PQ). * A vertical double-headed arrow labeled "h₂" indicates the vertical distance from point A (which is at MN) down to the bottom base of the submerged part of the cylinder in this state. * The setup rests on a horizontally hatched surface representing the ground.