gaokao 2017 Q4

gaokao · China · national-II-science Not Maths
4. As shown in the figure, on grid paper with unit squares, the three-view of a geometric solid obtained by cutting off part of a cylinder with a plane is shown. The volume of this geometric solid is
A. $90 \pi$
B. $63 \pi$
C. $42 \pi$
D. $36 \pi$ [Figure] [Figure]
5. Let $x , y$ satisfy the constraints $\left\{ \begin{array} { l } 2 x + 3 y - 3 \leqslant 0 , \\ 2 x - 3 y + 3 \geqslant 0 , \\ y + 3 \geqslant 0 , \end{array} \right.$ then the minimum value of $z = 2 x + y$ is
A. $-3$
B. $- 9$
C. $1$
D. $9$
4. As shown in the figure, on grid paper with unit squares, the three-view of a geometric solid obtained by cutting off part of a cylinder with a plane is shown. The volume of this geometric solid is\\
A. $90 \pi$\\
B. $63 \pi$\\
C. $42 \pi$\\
D. $36 \pi$\\
\includegraphics[max width=\textwidth, alt={}, center]{cd808fdb-5cf6-4ceb-9628-959ae73784cb-1_322_438_1552_1588}\\
\includegraphics[max width=\textwidth, alt={}, center]{cd808fdb-5cf6-4ceb-9628-959ae73784cb-1_203_341_1888_1585}

5. Let $x , y$ satisfy the constraints $\left\{ \begin{array} { l } 2 x + 3 y - 3 \leqslant 0 , \\ 2 x - 3 y + 3 \geqslant 0 , \\ y + 3 \geqslant 0 , \end{array} \right.$ then the minimum value of $z = 2 x + y$ is\\
A. $-3$\\
B. $- 9$\\
C. $1$\\
D. $9$