Question

Find the dimensions of a closed rectangular box with a square base and volume 2744 incubed that can be constructed with the least amount of material.

Answer 1

The dimensions of the closed rectangular box are  14 by 14 by 14

Step-by-step explanation:

Volume of the box will be : l×w×h  but l=w,hence volume= w²h

Area of the box is : 2w² + 4hw

Volume,v=w²h=2744----------find height,h

h=2744/w²-------------use this height in the area equation as;

Area=2w²+4hw

$A=2w^2+4(\frac{2744}{w^{2} } )*w\\\\\\A=2w^2+\frac{10976}{w}$

Minimizing the area

$dA/dw=4w-10976/w^2\\\\\\4w-10976/w^2=0\\\\\\4w^3-10976=0\\\\4w^3=10976\\\\w^3=2744\\\\w=\sqrt[3]{2744}\\ \\\\w=14$

w=15,to find the height use h=2744/w²

h=2744/14²

h=14

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Volume of a rectangular box :https://brainly.com/question/1414246

Keywords : volume

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