Question

A suitcase with measures $80cm\times 48cm\times 24cm$ 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 $\left(b\right)=48cm$
And Height of cuboidal box $\left(h\right)=24cm$

Since, suitcase covered with a tarpaulin cloth, we have to find Total surface area of suitcase.
Total surface area of suitcase box $=2(lb+bh+hl)$
$=2(80cm\times 48cm+48cm\times 24cm+24cm\times 80cm)$
$=2(3840c{m}^2+1152c{m}^2+1920c{m}^2$
$=2\times 6912c{m}^2$

$=13824c{m}^2$

Area of Tarpaulin cloth $=$ Surface area of suitcase
$\Rightarrow l\times b=13824c{m}^2$

It is given that, width of the Tarpaulin cloth is $96cm$

$\Rightarrow l\times 96cm=13824c{m}^2$

$\Rightarrow l=\frac{13824c{m}^2}{96cm}$

$\Rightarrow l=144cm$
Required tarpaulin cloth for $100$ suitcases

$=144cm\times 100$

$=14400cm$

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