Find the dimensions of a closed rectangular box with a square base and volume in that can be constructed with the least amount o

Question

alexdok [17]

1 year ago

7

Find the dimensions of a closed rectangular box with a square base and volume in that can be constructed with the least amount o

f material.

Mathematics

1 answer:

viva [34] · Answer 1 · 2024-07-18T03:01:34+03:00

The dimensions of a closed rectangular box are mathematically given as

w=14

h=14

This is further explained below.

<h3>Find the dimensions of a closed rectangular box:</h3>

In the geometry of the plane based on Euclidean theory, a rectangle is a quadrilateral that has four right angles.

It is also possible to refer to it as a parallelogram with a right angle or an equiangular quadrilateral. Equiangular refers to a quadrilateral in which each of its angles is equal to the others in the quadrilateral.

Generally, the equation for Area the is mathematically given as

Area=2w²+4hw

Therefore

$A=2 w^2+4\left(\frac{2744}{w^2}\right) * w\\\\$$$$A=2 w^2+\frac{10976}{w}\\\\$$$$d A / d w=4 w-10976 / w^2\\\\$$$$w=\sqrt[3]{2744}\\\\$$$$w=14$

In conclusion, Where h is

h=2744/w²

Hence

h=2744/14^2

h=14