The volume of largest possible right circular cylinder that can be increased in sphere of radius root3 is
Answers (2)
18th Apr, 2020
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
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
Comments (0)
18th Apr, 2020
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!
Comments (0)
