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.

Question

Volume =

i know it's in cubic centimeters. but i'm getting my values wrong

Answer 1

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

Answer 2

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

Answer 3

after that do i convert it to cubic centimeters? and if so, do i just do it to the 3rd power?

Answer 4

no

v = w^2 h = (2300/3) h

but h = (2300 -w^2)/4w

Answer 5

oh I completely forgot that you need to plug it in. Thank you so much. i got y answer as 10614.02