解决这道题，并生成解析---**Extraction Content:**
**Question Stem:**
如图是某多面体的三视图,尺寸如图,则该几何体的体积是( )
**Image Description:**
Three orthographic views of a solid.
* **正(主)视图 (Front View):** A square with side length 2. A diagonal dashed line runs from the top-left corner to the bottom-right corner. The square is divided into two parts by a horizontal dashed line from the left edge, 1 unit from the top edge. The top part above this dashed line has a vertical dashed line from the top edge, 1 unit from the left edge. The dimensions are labeled: 1, 1 on the top edge, and 1, 1 on the left edge.
* **左(侧)视图 (Left View):** A square with side length 2. A diagonal solid line runs from the top-left corner to the bottom-right corner. A dashed line runs horizontally from the left edge to the diagonal line, 1 unit from the top edge. The dimensions are labeled: 1, 1 on the top edge and 1, 1 on the left edge.
* **俯视图 (Top View):** A square with side length 2. A diagonal dashed line runs from the top-right corner to the bottom-left corner. A dashed line runs vertically from the top edge to the diagonal line, 1 unit from the left edge. The dimensions are labeled: 1, 1 on the top edge and 1, 1 on the left edge.
**Options:**
A. 6.5
B. 20/3
C. 47/6
D. 3.5
**Solution:**
【答案】
A
**Analysis/Explanation:**
【解析】
由题得该几何体为一个正方体被切去一个大角和一个小角,运用体积公式计算即可。
(详解)由题可知该几何体为一个正方体被切去一个大角和一个小角,如图, 该几何体的体积为
**Diagram Description in Explanation:**
A 3D isometric view of a cube with dashed lines representing the original cube edges and solid lines showing the resulting solid. The solid appears to be a cube with two corners cut off. One corner is cut off by a plane intersecting three faces at vertices, forming a triangle. Another smaller corner is cut off by a plane intersecting three faces at points along edges. The solid lines represent the visible edges of the resulting geometry.
**Mathematical Formula/Calculation:**
V = 2 x 2 x 2 - (1/3) x (1/2) x 2 x 2 x 2 - (1/3) x (1/2) x 1 x 1 x 1 = 8 - (1/3) x 4 - (1/3) x (1/2) = 8 - 4/3 - 1/6 = 48/6 - 8/6 - 1/6 = (48 - 8 - 1)/6 = 39/6 = 13/2 = 6.5
**Conclusion:**
故选: A