Question

A cylindrical drum with an open top is to be constructed using 1 m^2 of aluminum
a)write and equation for the volume of the drum in terms of radius
b)what radius gives the direct maximum value?
c)What is the maximum volume if the radius can be a maximum of 0.2m ?
c)

Answer 1

no ideas at all

v = pi r^2 h
so, h = (1/pi r^2)

to find max volume,

dv/dt = 2pi r h
now plug in the value for h, and solve for dv/dr = 0

Answer 2

just to be precise, h = 1/(pi r^2)