Question

What is the volume of a box?​

Answer 1

Volume = (4x³ - 114x² + 800x) cm³

Explanation:

In geometry, a net is a 2D shape that can be folded to form a 3D shape or a solid.

The given figure is the net of a box with dimensions:

• Width = (25 - 2x) cm
• Length = (32 - 2x) cm

The box can be modelled as a rectangular prism.

`\boxed{\begin{minipage}{5 cm}\underline{Volume of a rectangular prism}\\\\$V=w\:l\:h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

Assuming the height of the box is x cm, substitute the given values into the formula:

`\begin{aligned}\implies \textsf{Volume} & = \sf width * length * height\\& = (25-2x)(32-2x)x\\& = (800-114x+4x^2)x\\& = 4x^3-114x^2+800x\end{aligned}`

Therefore, the expression for the volume of the box is:

`\large\boxed{(4x^3 -114x^2 + 800x) \; \sf cm^3}`