00:01
If the volume of a sphere and a cylinder are equal, then that means that four -thirds pi -r cubed, where this little r is the radius of the sphere, must be equal to pi big r, where squared, where big r is the radius of the circle and the cylinder, times l, where l is the height of the cylinder.
00:26
The ratio of surface areas will denote this, says s sub r will be equal to 4 pi r squared divided by 2 pi r l plus 2 pi r squared.
00:49
From the ratio of the volumes, we know that l must be equal to 4 thirds r cubed over little r squared.
01:02
That means our surface area will become 4 pi r squared divided by 2 pi capital r 4 thirds little r cubed over capital r squared plus 2 pi capital r squared removing 2 pi capital r squared from the whole denominator will give us to r squared over capital r squared divided by four thirds, little r cubed over capital r cubed plus one.
01:56
Thus, if we define a ratio of the diameters of the sphere and the cylinder to be r over capital r, then this will become in terms of the ratio of the diameters to d squared over four thirds d cubed plus one.
02:19
So that's the answer to the first part of the question.
02:22
We are now asked to find if there is any minima or maxima of this ratio...