me, the main dish (pièce de résistance : the hard part, which will resist the most)

Pièce de résistance (in a meal) is more comonly called "le plat" or "le plat principal".

The circumference of a circle: C = 2(pi)r

The area of a circle: A = (pi) r^2

C = 25.12 cm

2(pi)r = 25.12 cm

r = 25.12/[2(pi)]

r = 12.56/pi

r^2 = 157.7536/pi^2 So,

A = (pi)r^2

A = (pi)(157.7536/pi^2)

A = 157.7536/pi

A = 50.22 cm^2 (approximately)

girth = 2PI r

height=h

h+2 PI r =108

h=108-2 PI r

Volume = PI r^2 h

V = PI r^2 (108-2PI r)

Differentiate with respect to r

dV/dr = PI (2r) (108-2PI r) +PI r^2 (-2PI) =0

216 PI r -4 PI^2 r^2 -2 PI^2 r^2=0

216 PI r -6 PI ^2 r^2=0

PI r [ 216-6 PI r] =0

6 PI r = 216

r = 36/PI --- dimensions

h = (108-2 PI (36/PI)) = 108 -72=36 -- dimensions

Largest volume = PI r^2 h = PI (36/PI)^2 (36)

=1,296 / PI

d^2V/dr^2 =216 PI -6 PI^2 (2r)

when r=36/PI, d^2V/dr2 = 216 PI - 6PI^2 (2)(36)/PI

=216 PI -432 PI < 0, indicates V has been maximized.