Open Top
If 1800 sq. cm of material is available to make a box w/ a square base & an open top, find the largest volume?
If 1800 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 = cubic centimeters?
a = area
b = base
h = height
v = volume
a = 1800
a = b^2 + 4hb
v = b^2*h so h = v/b^2
1800 = b^2 + 4vb/b^2 = b^2 + 4v/b
1800b = b^3 + 4v
450b – (b^3)/4 = v
dv/db = 450 – (3/4)b^2
b^2 = (4/3)*450
b = sqrt(600)
a = 1800 = 600 + 4*root(600)*h
1200 = 4 * root(600) * h
h = 300/root(600)
v = root(600) * root(600) * 300/root(600)
v = root(600) * 300
v = 300 * root(600) =
Max Volume = 7348.47 cm^3
Hope I helped.
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