Area = x^2 + 4xy = 2100
y = (2300 -x^2)/(4x) = (525/x) - (x/4)
Volume = y*x^2 = 525x -(x^3/4)
dV/dx = 0 = 525 - (3/4)x^2
x = sqrt 733.3 = 26.45 cm
y = 13.24 cm
max volume = 14,410 cm^3
unless i added wrong
If 2300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume =
i know it's in cubic centimeters. but i'm getting my values wrong
5 answers
v = w^2 h
A = 2300 = w^2 + 4 w h
4 w h = 2300 - w^2
h = (2300 -w^2)/4w
so
v = w^2 [ (2300 -w^2)/4w ]
v = 2300 w/4 - w^3/4
4 dv/dw = 2300 -3 w^2 = 0 for max
w^2 = 2300/3
w = 27.7 cm
etc
A = 2300 = w^2 + 4 w h
4 w h = 2300 - w^2
h = (2300 -w^2)/4w
so
v = w^2 [ (2300 -w^2)/4w ]
v = 2300 w/4 - w^3/4
4 dv/dw = 2300 -3 w^2 = 0 for max
w^2 = 2300/3
w = 27.7 cm
etc
after that do i convert it to cubic centimeters? and if so, do i just do it to the 3rd power?
no
v = w^2 h = (2300/3) h
but h = (2300 -w^2)/4w
v = w^2 h = (2300/3) h
but h = (2300 -w^2)/4w
oh I completely forgot that you need to plug it in. Thank you so much. i got y answer as 10614.02