Hi,

r^2=R^2-(h^2)/4
Vc=pie r^2 h
=Pie(R^2-(h^2)/4)h

dV/dh=pie R^2 - (3pie h^2)/4
For R=root 3
dV/dh= 3pie - (3pie h^2)/4
For maximum or minimumvolume,dV/dh=0
h=2

Also,dhdVchanges sign from positive to negativein the neighbourhood ofh=2. Hence,h=2is a maximum point.
r= root 2
V=4 pie cubic units

Hey,

it is given radius of sphere is root3.

we know that,

r^2= R^2 - ((h^2)/4)

Vc= pi*r^2*h = pi*(R^2-((h^2)/4)h=pi*R^2*h-(pi*h^3/4)

Now

dV/dh=pi*R62-3*pi*h^2/4

for maximum or minimum volume we know that dV/dh=0

hence putting the value of dV/dh and R=root 3 in above equation we get,

h=2

if h=2 then

r= root 2

and volume is equal to 4pi cubic units

which is the required answer.

I hope this helps.

all the best!