Question

An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.

Answer 1

The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,

Volume of the box = length × width × Height

12 = 5x² × H

H= 12 / 5x²

Further, the surface area of the open box is,

Surface area of the box

$= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}$

Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).

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