Question

A open cylindrical wastepaper bin, of radius r cm and volume V cm^3, is to have a surface area of 5000cm^3.
a.Show that V=1/2 *r(5000-pir^2)
b.Calculate the maximum possible capacity of the bin.

Answer 1

let the height be h cm
SA = circular base + rectangular sleeve
= πr^2 + 2πrh
= 5000
2πrh = 5000 - πr^2
h = (5000-πr^2)/(2πr)

V= πr^2 h
= πr^2((5000-πr^2)/(2πr))
= (1/2)r(5000-πr^2) as asked for
= 2500r - πr^3/2
dV(dr) = 2500 - (3/2)π r^2 = 0 for a max of V
(3/2)πr^2 = 2500
r^2 = 5000/(3π)
r = √( 5000/(3π) ) = ....
Now go to your calculator, so far there was no need for it

check my algebra, I did not write it out on paper first