# Calculus

A rectangular box has a square base whose edge has length at least one centimeter, and its total surface area is 600 cm2. What is the largest possible volume that such a box can have?

V = 500 in3
V = 750 in3
V = 900 in3
V = 1,000 in3

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1. 2 x^2 + 4 x h = 600
h = (600 -2 x^2 )/4x or h = (300 - x^2)/2x

v = x^2 h
v = (1/2)( x)(300 -x^2)
v = (1/2)(300 x - x^3)
dv/dx = (1/2) (300 - 3 x^2) = 0 for max or min
so
x = 10
then x^2 = 100
h = 10
v x^2h = 1000

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posted by Damon

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