Question
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Answers
If we have base x^2 and height y,
2x^2 + 4xy = 600
v = x^2y = x^2(600-2x^2)/4x
= 150x - x^3/2
Now just find x where v' = 0
2x^2 + 4xy = 600
v = x^2y = x^2(600-2x^2)/4x
= 150x - x^3/2
Now just find x where v' = 0
0.0
20000
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