Question

欲做一个容积为8π的开口圆柱形容器,问底半径和高为多少时用材最省

Answer 1

let

r be the radius

h be the height

V= πr^2h = 8π

h=8/r^2

A = πr^2 + 2πrh

= πr^2 + 16π/r

A' =π(2r-16/r^2)=0

2r^3-16=0

r=2

A'' =π(2+32/r^3)

A''(2)>0 ( min )

min A at r =2

h=8/r^2

= 2