A rectangular storage container is to have a volume of 10m c

Solution

V=10m³

Dim:

w x 2w x h

V= 2w²h=10     this gives h=5/w²

Amount of material needed is the surface area:

SA=2(w*h)+2*(w*2w)+2(2w*h)

=2(w*5/w²)+2(2w²)+2(2w*5/w²)

=10/w+4w²+20/w

=30/w+4w²

To find minimum, take the derivative of SA.

d(SA)/dw= -30/w²+8w

We will find minimum when the above equals 0.

Min:

-30/w²+8w=0

8w=30/w²

8w³=30

w³=15/4

w=(15/4)^1/3=1.55m

l=2(15/4)^1/3=3.11m

h=5/4(15/4)^2/3=2.07