Question
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
Answers
oobleck
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
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
yup
how did you get 88/3? and 85184n? don't get it