Question

A suitcase with measures$80cmx48cmx24cm$ is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width $96cm$ is required to cover $100$ such suitcases?

Answer 1

Given

Length of suitcase box $\left(l\right)=80cm,$

Breadth of suitcase box$\left(b\right)=48cm$

Height of cuboid box $\left(h\right)=24cm$

Find out

We have to find out how many meters of tarpaulin are required

Formula

$Totalsurfaceareaofsuitcasebox=2\times (lb+bh+hl)$

$$\begin{gathered} =2\times (80\times 48+48\times 24+24\times 80) \\ =2\times (3840+1152+1920) \\ =2\times 6912 \\ =13824cm² \end{gathered}$$

Hence, the Total surface area of the suitcase box is $13824cm²$

As the suitcase is fully covered by a tarpaulin

$$\begin{gathered} AreaofTarpaulincloth=Surfaceareaofsuitcase \\ (l\times b)=13824 \\ (l\times 96)=13824 \\ l=144m \end{gathered}$$

Required tarpaulin for $100$ suitcases $=144\times 100=14400cm=144m$

Hence, the tarpaulin cloth required to cover $100$ suitcases is $144$ m.