find dimension of cylinder of the greatest area lateral surface area that can inscribed a sphere if radius=6m

Answer 1

If you call x =half of the height of the cilindet the radius of the base would be
r=sqrt(36-x^2) and the lateral surface
S= 2pi*sqrt(36-x^2) * 2x=4pi* x*sqrt(36-x^2)
S´= sqrt(36-x^2) -x^2/sqrt(36-x^2)=0
36-2x^2=0 x^2=18 and x= 3sqrt(2) The sign is+++ x---------
So the dimensions are
height= 6sqrt(2)m=8.49m
radius of the base 3sqrt2m
The height and the diameter of the base are equal