an open rectangular box with volume 6 m^3 has square base.?

express the surface area of the box as a function of the length (x) of a side of the base.

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A few days ago

veteris

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First lets find the dimentions of the box.

The base is a square so, the width and the length are x. To find the height, we need to use the volume and the area of the base.

The volume of the box can be found with the equation:

V = lbh

but l and b are eual to x, and V is 6, so:

6 = x * x * h

6=(x^2)h

there fore h = 6/(x^2)

Now the box is open so there is no top, so the base only has one square:

(1) A=x*x=x^2

Now the sides. There are 4 sides who are x by the height, 6/(x^2).

The Area of one is: A = x * 6/(x^2) = 6/x

The area of the four (2) A= 4*6/x = 24/x

So the total surface area is SA =( x^2 + 24/x ) m^2

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