a rectangle PQRS with the length v-cm and the width z-cm and its perimeter 88cm. the rectangle is axis of symmetry and parallel to RS to generate cylinder. find the maximum value of its volume

Answer 1

Draw the rectangle with vertices at P=(0,0) Q=(v,0) R=(v,z) S = (0,z)
The axis of symmetry is the line y = z/2
We have v+z = 44
You don't say how PQRS is rotated, but I assume it is around the axis of symmetry, so its volume is
v = π(z/2)^2 v = π(z/2)^2(44-z) = π/4 (44z^2 - z^3)
dv/dz = π/4 (88z - 3z^2)
dv/dz = 0 when z = 88/3
so max v = 85184π/27

Answer 2

how did you get 88/3? and 85184n? don't get it