gaokao 2022 Q12

gaokao · China · national-B-arts 5 marks Stationary points and optimisation Geometric or applied optimisation problem

A sphere $O$ has radius 1. A pyramid has its apex at $O$ and the four vertices of its base all on the surface of sphere $O$. When the volume of this pyramid is maximized, its height is
A. $\frac { 1 } { 3 }$
B. $\frac { 1 } { 2 }$
C. $\frac { \sqrt { 3 } } { 3 }$
D. $\frac { \sqrt { 2 } } { 2 }$

A sphere $O$ has radius 1. A pyramid has its apex at $O$ and the four vertices of its base all on the surface of sphere $O$. When the volume of this pyramid is maximized, its height is

A. $\frac { 1 } { 3 }$

B. $\frac { 1 } { 2 }$

C. $\frac { \sqrt { 3 } } { 3 }$

D. $\frac { \sqrt { 2 } } { 2 }$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21