Let $\sqrt{3}$ be the radius and $\frac{\pi}{3}$ be the semi-vertical angle of the given cone. Then, the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is

If an error of $0.02 \mathrm{sq} . \mathrm{cm}$ is found in the surface area of a sphere when its radius is measured as 10 cm , then the approximate error that occurs in the volume of the sphere, in cubic centimeters, is

If $\theta$ is the angle between the curves $y^2=4 x$ and $x^2+y^2=5$, then $|\tan \theta|=$

The local maximum value of the function $f(x)=-(x-2)^3(x+2)^2$ is