Question

A rectangular box open at top has a volume of 108 cubic feet. Find the dimensions if the surface area is minimum

Answer 1

Answer:

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Answer 2

Given:

The volume of the rectangular box open at the top = 108 cubic feet

The surface area of the box is minimum

To find:

The dimensions of the rectangular box

Solution:

It is mentioned in the question that the rectangular box has the minimum surface area.

For a rectangular box to be of the minimum surface area all the sides will be of equal length hence it will have all square faces.

Also, it is given that the box is open on top, hence the surface area will be of 5 square sides only.

Now, The volume of the box = 108 cubic feet

Let the side of the cube be 'a' feet.

The volume of box = $a^3$

$a^3$ = 108

a = 4.76

Therefore the dimensions of the rectangular box will be 4.76 feet.