Question

The measurements of a luggage box are $48\mathrm{cm},36\mathrm{cm},28\mathrm{cm}$. Find the volume of the box. How many square centimeters of cloth is required to make a cover for the box?

Answer 1

Step 1: Calculate the volume of the box.

Let the length, breadth, and height of the box is $l,b$, and $h$respectively.

Given,

$l=48\mathrm{cm},b=36\mathrm{cm},h=28\mathrm{cm}$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{box}=l\times b\times h \\ \Rightarrow =48\times 36\times 28 \\ \Rightarrow =48384{\mathrm{cm}}^3 \end{gathered}$$

Hence, the volume of the box is $48384{\mathrm{cm}}^3$.

Step 2: Calculate the surface area of the box.

To find the cloth required to make a cover for the box, we have to find the surface area of the box.

$$\begin{gathered} \therefore \mathrm{Surface}\mathrm{area}=2\left(lb+bh+hl\right) \\ \Rightarrow =2\left[(48\times 36)+(36\times 28)+(28\times 48)\right] \\ \Rightarrow =2\left[1728+1008+1344\right] \\ \Rightarrow =2\times 4080 \\ \Rightarrow =8160{\mathrm{cm}}^2 \end{gathered}$$

Hence, the cloth required is $8160{\mathrm{cm}}^2$ to make a cover for the box.