Question

A hundred cubicle cardboard boxes are required in a Jewellery shop. The length of the edge of each box must measure 15cm. How many cardboard sheets of size $30cm\times 30cm$ will be required to make these boxes?

Answer 1

Hint: To solve this question, we will first find out the total surface area of each cardboard and then we will divide this by area of cardboard and then we will divide this by area of cardboard sheet to get the total number of sheets required.

Complete step-by-step answer:
To get the total number of sheets required to make 100 cubicle cardboard boxes of edge length each, we will first determine the area of each face of the cubical cardboard. As the face of the cubes is a square the area of this face is given by:
$\begin{aligned} & Area={{\left( edge \right)}^{2}} \\\ & area\,of\,one\,face={{\left( 5cm \right)}^{2}} \\\ & \Rightarrow Area\,of\,one\,face=225c{{m}^{2}}\, \\\ \end{aligned}$
Now, there are 6 faces on a cubical box. So, the total area of all the faces of a cubical box
$\begin{aligned} & 6\times 225c{{m}^{2}} \\\ & =1350c{{m}^{2}} \\\ \end{aligned}$
Now, it is given that there are 100 such cubicle cardboard boxes. The area of one cardboard cubical box = $1350c{{m}^{2}}$. So, the total surface area of the 100 cubicle cardboard boxes
$\begin{aligned} & 1350\times 100 \\\ & =13500c{{m}^{2}} \\\ \end{aligned}$
Now, we have to find the area of each sheet. The dimensions of that are $30cm\times 30cm$. As the cardboard sheet is square in shape, the total area of one sheet will be=
$\begin{aligned} & Area={{\left( edge \right)}^{2}} \\\ & \Rightarrow area\,of\,one\,cardboard\,sheet={{\left( 30cm \right)}^{{2}}}={900cm^2} \\\ & \\\ \end{aligned}$
Now, to obtain the total number of cardboard sheets, we will divide the total area of cardboard cubicle boxes by the total area of one sheet. Thus, the total number of sheets are given by:
$\begin{aligned} & total\,number\,of\,sheets=\dfrac{Total\,number\,of\,cardboard\,boxes}{area\,of\,one\,cardboard\,sheet} \\\ & =\dfrac{135000c{{m}^{2}}}{900c{{m}^{2}}} \\\ & =150sheets \\\ \end{aligned}$
So we will need 150 sheets to make 100 cubicle cardboard boxes.

Note: The direct method for this would have been as shown: first we will calculate how many sheets we will require to make one cardboard box and then to obtain a total number of sheets, we will multiply it by 100. In our case 1.5 sheets is required to make one box, so, to make 100 boxes, we will need $1.5\times 100=150\,sheets$.