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