You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area? Keep your answer in radical form and omit units.

Question
Asked Oct 31, 2019

You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area? Keep your answer in radical form and omit units.

check_circleExpert Solution
Step 1
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Step 2
Use the equation (1 ) to find the value of h in terms ofx as follows.
xh 184
( V184)
184
h=
184
in A x4xh
Substitute h .
184
A =x24x
184
=x2 +4
x
736
help_outline

Image Transcriptionclose

Use the equation (1 ) to find the value of h in terms ofx as follows. xh 184 ( V184) 184 h= 184 in A x4xh Substitute h . 184 A =x24x 184 =x2 +4 x 736

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Step 3
736
with respect to x
Differentiate A = x+
736
d
2
dA
736
=2x
Equate the derivative to zero.
736
2x
0
736
2x
736
2
x = 7.2
help_outline

Image Transcriptionclose

736 with respect to x Differentiate A = x+ 736 d 2 dA 736 =2x Equate the derivative to zero. 736 2x 0 736 2x 736 2 x = 7.2

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