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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