Question help

[dianzhang]

make a box with base length twice its base width and box has a capacity of 5.0 m^3 (5000 L)
find the dimensions so less material is used up.


MOD edit: Removed random poll and changed topic name to make it make sense

[hermish]

Surface area = 2*L*w + 2*w*h +2*L*h
L = Length
w = width
h = height

L = 2w ( given)
L x w x h = 5 ( given)

L = 2w x w x h = 2w^2 x h
h = 5/(2w^2)

Back to surface area equation. replace L with 2w and h with h = 5/(2w^2)
Surface area = 4w^2 + 15/w

Differentiated surface area = 8w - (15/w^2)

let differentiated equation equal to 0 and solve for w
w = sqrt(30)/ 4

Therefore L = sqrt(30)/2
h=4/3

[dianzhang]

Surface area = 2*L*w + 2*w*h +2*L*h
L = Length
w = width
h = height

L = 2w ( given)
L x w x h = 5 ( given)

L = 2w x w x h = 2w^2 x h
h = 5/(2w^2)

Back to surface area equation. replace L with 2w and h with h = 5/(2w^2)
Surface area = 4w^2 + 15/w

Differentiated surface area = 8w - (15/w^2)

let differentiated equation equal to 0 and solve for w
w = sqrt(30)/ 4

Therefore L = sqrt(30)/2
h=4/3

i managed to figure it out later by the way.
you were right up to the point there you let the differentiated surface area = 0
but w does not equal sqrt(30)/4
w actually equals cbrt(15/8) and it'll give you the answer of 1.23m
therefore L = 2.37m and h = 1.64m
thanks anyway dude