<span>we know the surface area of the two ends of the closed cylinder
is: 2 (r</span>2) .
<span>The surface are of the side
of the cylinder is h (2r)</span>
<span>So the total surface area is: 2 ( r</span>2<span>) + h (2 r )</span>
<span>The volume of the cylinder is r</span>2 h = 40 cm3
now solve this last equation
for h:
<span>so, h = 40 / (*r</span>2)
Substitute the value for h
into the expression for the total surface area:
<span>2 ( r</span>2<span>) + (40 / ( r</span>2<span>)) (2 r )</span>
Now Simplify the above
expression we get:
<span>2 ( r</span>2) + (80 / r)
Now take the derivative:
<span>4 r - 80 r </span>-2
Set it equal to zero and
solve for r:
<span>4 r - 80 r </span>-2 = 0
Divide by 4:
*r - 20 r -2 = 0
Multiply by r2 we
get:
r3 - 20 = 0
r3 = 20
r3 =
20/
Hence,
<span>r = (20 / )</span>(1/3)
r 1.8534 cm
<span>Substitute this value for r into h = 40 / ( r</span>2) and evaluate h:
<span>h = 40 / *(1.8534)</span>2
h 3.7067
<span> </span>
