gaokao 2022 Q9

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

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

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

Paper Questions

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