SOLUTION: I am in College Algebra but the question seemed to fit in this category...The base and sides of a container are made of wood panels. The container does not have a top. The base and

Question 1099839: I am in College Algebra but the question seemed to fit in this category...The base and sides of a container are made of wood panels. The container does not have a top. The base and sides are rectangular. The width is x cm. The length is 4 times the width. The volume is 600 cm^3. Determine the minimum surface area to two decimal places.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The container does not have a top.
The base and sides are rectangular.
The width is x cm. The length is 4 times the width.
The volume is 600 cm^3.
Determine the minimum surface area to two decimal places.
:
let h = the height of the box
Given
x = the width
4x = the length
Volume
4x * x * h = 600
4x^2 * h = 600
h =
cancel the 4
h =
:
Surface area
S.A. =(4x*x) + 2(4x*h) + 2(x*h)
S.A. = 4x^2 + 8xh + 2xh
S.A. = 4x^2 + 10xh
replace h with
S.A. = 4x^2 + 10x*
Cancel x
S.A. = 4x^2 +
plot the equation y = 4x^2 + (1200/x), where y = the surface area

You can see minimum surface area occurs when x = 5.2 cm. Green: y=339
Find the minimum surface area
S.A. = 4(5.2^2) +
S.A. = 108.16 + 230.77
S.A = 338.93 sq/cm

Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
Since the tutor @ankor@dixie-net.com made several mistakes in his solution, I re-write and edit it in correct way.

The container does not have a top. The base and sides are rectangular. The width is x cm. The length is 4 times the width. The volume is 600 cm^3. Determine the minimum surface area to two decimal places. : let h = the height of the box Given x = the width 4x = the length Volume 4x * x * h = 600 4x^2 * h = 600 h = cancel the 4 h = <<<---=== I replaced 120 by 150 : Surface area S.A. =(4x*x) + 2(4x*h) + 2(x*h) S.A. = 4x^2 + 8xh + 2xh S.A. = 4x^2 + 10xh replace h with S.A. = 4x^2 + 10x* Cancel x S.A. = 4x^2 + plot the equation y = 4x^2 + (1500/x), where y = the surface area Taking the derivative y' = 8x - 1500/x^2 = , <<<---=== I re-wrote this part you will find the minimum surface area occurs when x = = 5.72 Find the minimum surface area S.A. = Answer S.A. = 393.1 cm^2.

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