Answer:
Dimensions will be 4 * 2 cm.
Step-by-step explanation:
l = length of rectangle and w = width
Perimeter = 2l + 2w = 12
l + w = 6.
---> l = 6 - w
Volume of the cylinder
V = πr^2l
w = 2πr
--> r = w/2π
l = 6 - w so
V = π(w/2π)^ 2 * (6 - w)
---> V = w^2/4π (6- w)
---> V = 3w^2/ 2π - w^3/4π
Differentiating:
dV/ dw = 6w/ 2π - 3w^2 / 4π
= - 3(w - 4)w / 4π
This equals 0 for maximum volume
- 3(w - 4)w / 4π = 0
w = 0 or w = 4
