Q. 204.1( 66 Votes )
Show that the rig
Answer :
Let r be the radius and h be the height of the cylinder.
Then, the surface area (S) of the cylinder is given by:
S = 2πr2 + 2πrh
⇒ h
Let V be the volume of the cylinder. Then
V = πr2h
Now,
If
So, when then
<0
Then, by second derivative test, the volume is the maximum when
Now, when . then h =
Therefore, the volume is the maximum when the height is the twice the radius or height is equal to diameter.
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