ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: dianzhang on February 15, 2012, 09:36:15 pm
-
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
-
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
-
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 :)