Question

2 Show that the height of a
closed circular
cylinder of given total surface area and
maximum volume is equal to the diameter
of its base ​

Answer 1

Answer:

Let S and V dente the surface and volume of the right circular cylinder of height h and base radius r. Then

S=2πrh+2πr

2

⟶(1)

V=πr

2

h

=πr

2

(

2πr

S−2πr

2

)

=

2

r

(S−2πr

2

)=

2

Sr

−πr

3

dr

dV

=

2

S

−3πr

2

=0 for max or min S=6πr

2

Substituting S=6πr

2

in equation (1)

6πr

2

=2πr

2

+2πrh

⇒2r=h

Also

dr

2

d

2

V

=−6πr

dr

2

d

2

V

at r=h/2=−3πh<0

Hence volume is maximum when height is equal to diameter of the base.

Step-by-step explanation:

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