Volume from Three-View or Cross-Section Diagram

The question provides orthographic projection views (front, side, top) or a described cross-sectional profile of a geometric solid and asks the student to determine its volume.

gaokao 2015 Q5 5 marks View
The three views of a certain solid are shown in the figure. The volume of this solid is
(A) $\frac { 1 } { 3 } + 2 \pi$
(B) $\frac { 13 \pi } { 6 }$
(C) $\frac { 7 \pi } { 3 }$
(D) $\frac { 5 \pi } { 2 }$
gaokao 2015 Q5 View
5. The three-view drawing of a certain solid is shown in the figure. The volume of this solid is
[Figure]
Front view
[Figure]
Left view
[Figure]
Top view
A. $\frac { 1 } { 3 } + \pi$
B. $\frac { 2 } { 3 } + \pi$
C. $\frac { 1 } { 3 } + 2 \pi$
D. $\frac { 2 } { 3 } + 2 \pi$
gaokao 2015 Q10 View
10. The three-view drawing of a workpiece is shown in Figure 3. The workpiece is to be machined by cutting into a rectangular parallelepiped with the largest possible volume, with one face of the new workpiece lying on a face of the original workpiece. Then the material utilization rate of the original workpiece is (material utilization rate = volume of new workpiece / volume of original workpiece) [Figure]
A. $\frac { 8 } { 9 \pi }$
B. $\frac { 8 } { 27 \pi }$
C. $\frac { 24 ( \sqrt { 2 } - 1 ) ^ { 3 } } { \pi }$
D. $\frac { 8 ( \sqrt { 2 } - 1 ) ^ { 3 } } { \pi }$
II. Fill-in-the-Blank Questions: This section has 5 questions, each worth 5 points, for a total of 25 points
gaokao 2015 Q10 View
10. The three-view drawing of a workpiece is shown in Figure 3. The workpiece is to be machined by cutting into a rectangular solid with the largest possible volume, with one face of the new workpiece lying on a face of the original workpiece. The material utilization rate of the original workpiece is (Material utilization rate = Volume of new workpiece / Volume of original workpiece.) [Figure]
A. $\frac { 8 } { 9 }$
B. $\frac { 16 } { 9 }$
C. $\frac { 4 ( \sqrt { 2 } - 1 ) ^ { 2 } } { 9 }$
D. $\frac { 12 ( \sqrt { 2 } - 1 ) ^ { 2 } } { 9 }$
II. Fill-in-the-Blank Questions: This section has 5 questions, each worth 5 points, for a total of 25 points