Question

A company has released the following possible designs for a new cereal box. The cost ofproduction depends upon the cost of materials, which is determined by how muchmaterial is used. The amount of material used is equal to the surface area of thepackage plus some overlap. The amount of product contained in the package is thevolume of the packaging.Find the surface area and volume of the following possible cereal boxes. Determine thecost of making the cereal box assuming that cardboard costs $0.05 per square inch.volume of box:surface area of box:cost of material:

Answer 1

Given

The sides of the cereal box is given

2 in, 7.5 in, 12 in.

Explanation

The volume of cereal box is

$V=l\times b\times h$

Substitute the values.

$\begin{gathered} V=12\times7.5\times2 \\ V=180in^3 \end{gathered}$

The surface area of cereal box is

$S=2lb+2bh+2hl$

Substitute the values

$S=2\times12\times7.5+2\times7.5\times2+2\times2\times12$$\begin{gathered} S=180+30+48 \\ S=258in^2 \end{gathered}$

Answer

The volume is 180 cubic in.

The surface area is 258 sq.in.