An open box with a square base is to have a volume of 20 ft3.(a) Find a function that models the surface area A of the box in terms of the length of one side of the base x. (b) Find the box dimensions that minimize the amount of material used. (Round your answers to two decimal places.)

Question
Asked Oct 10, 2019

An open box with a square base is to have a volume of 20 ft3.

(a) Find a function that models the surface area A of the box in terms of the length of one side of the base x.
 
(b) Find the box dimensions that minimize the amount of material used. (Round your answers to two decimal places.)
check_circleExpert Solution
Step 1

Let x be the side of the square base and y be the height of the...

Volume of base V = 20
xy 20
20
x
х*
Surface area of the box
A(x) x4xy
20
A(x)x+4x
80
4(x) x
x
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Volume of base V = 20 xy 20 20 x х* Surface area of the box A(x) x4xy 20 A(x)x+4x 80 4(x) x x

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Math

Calculus

Derivative