Question

A suitcase with measures 80 cm ×
48 cm × 24 cm is to be covered with
a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover
100 such suitcases?
Please give a detailed explanation

Answer 1

Given :

• Length of suitcase = 48 cm
• Breadth of suitcase = 80 cm
• Height of suitcase = 24 cm
• Width of tarpaulin = 96 cm

To find :

• How many tarpaulin is required to cover 100 suitcases.

According to the question,

$\sf : \implies{Total \: surface \: area \: of \: suitcase = 2(lb + bh + hl)}$

$\sf : \implies{2(48 \times 80 + 80 \times 24 + 24 \times 48) \: {cm}^{2} }$

$\sf : \implies{2(3840 + 1920 +1152) \: {cm}^{2} }$

${ \underline{ \boxed{ \sf \red{: \implies{13824 \: {cm}^{2} }}}}} \: \bigstar$

• So, the total surface area of suitcase is 13824².

Now,

$\sf: \implies{Area \: of \: 100 \: suitcases = 13824 \: {cm}^{2} \times 100 }$

${ \underline{ \boxed{\sf \blue{: \implies{1382400 \: cm {}^{2} }}}}} \: \bigstar$

So,

$\sf : \implies{Area _{ \: rectangular \: tarpaulin} = length \times breadth}$

$\sf : \implies{1382400 \: {cm}^{2} = l \times 96 \: cm}$

$\sf : \implies{ \dfrac{1382400}{96} \: cm = l}$

${ \underline{ \boxed{ \sf \orange{ : \implies{14400 \: cm}}}}} \: \bigstar$

Note :

As it is given in the question that we have to convert it in metres. So, the value is 144 m.

$\therefore{ \underline{ \sf{ \: \: \: So, \: { \textsf { \textbf{144 metres}}} \: of \: tarpaulin \: is \: required \: to \: cover \: 100 \: suitcases.}}}$

Answer 2

$\; \; \; \; \;{\large{\bold{\sf{\underline{Correct \; question}}}}}$

➙ A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

$\; \; \; \; \;{\large{\bold{\sf{\underline{\underbrace{Let's \; understand \; the \; question \; 1^{st}}}}}}}$

➙ This question says that there is a suitcase of dimensions 80 cm × 48 cm × 24 cm to be covered with a tarpaulin cloth. We have to find that how many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases? Means we have to find out answer in m ( need to change unit ) and the other all units are given in cm to us.

$\; \; \; \; \;{\large{\bold{\sf{\underline{Given \; that}}}}}$

Dimensions of suitcase

➙ Length of suitcase = 48 cm

➙ Breadth of suitcase = 80 cm

➙ Height of suitcase = 24 cm

And

➙ Breadth of tarpaulin = 96 cm

$\; \; \; \; \;{\large{\bold{\sf{\underline{To \; find}}}}}$

➙ How many metres of tarpaulin are required to cover 100 such suitcases?

$\; \; \; \; \;{\large{\bold{\sf{\underline{Solution}}}}}$

➙ 144 metres of tarpaulin are required to cover 100 such suitcases.

$\; \; \; \; \;{\large{\bold{\sf{\underline{Full \; Solution}}}}}$

$\rule{150}{1}$

✠ Let's start ( according to the question )

➨ TSA ( Total surface area ) of suitcase = 2(lb + hl + bh)

➨ TSA ( Total surface area ) of suitcase = 2(48 × 80 + 24 × 48 + 80 × 24)

➨ TSA ( Total surface area ) of suitcase = 2(3840 + 1152 + 1920)

➨ TSA ( Total surface area ) of suitcase = 2(4992 + 1920)

➨ TSA ( Total surface area ) of suitcase = 2(6912)

➨ TSA ( Total surface area ) of suitcase = 2 × 6912

➨ TSA ( Total surface area ) of suitcase = 13824 cm²

${\red{\sf{\boxed{TSA \: = \: 13824^{2} cm}}}}\pink\bigstar$

${\green{\frak{Henceforth, \: 13824^{2} \: cm \: is \: the \: TSA \: of \: suitcase}}}$

$\rule{150}{1}$

✠ Now let's find the area of 100 suitcase

➨ Area of 100 suitcase = 13824 cm² × 100

➨ Area of 100 suitcase = 1382400 cm²

${\red{\sf{\boxed{Area \: of \: 100 \: suitcase \: = \: 1382400^{2} cm}}}}\pink\bigstar$

${\green{\frak{Henceforth, \: 1382400^{2} \: cm \: is \: the \: area \: of \: 100 \: suitcases}}}$

$\rule{150}{1}$

✠ Now let's find the area of tarpaulin cloth ( rectangular shape )

➨ Area of cloth = L × B

Where,

➨ L denotes length

➨ B denotes Breadth

Putting the values,

➨ 1382400 = L × 96

➨ 1382400 / 96 = L

➨ 14400 = L

➨ L = 14400 cm

${\red{\sf{\boxed{Length \: = \: 14000 \: cm}}}}\pink\bigstar$

${\green{\frak{Henceforth, \: 14400 \: cm \: is \: L}}}$

$\rule{150}{1}$

➙ Means 14400 cm of tarpaulin are required to cover 100 such suitcases.

➙ But as the question says we have to find this in metres so let's convert

$\rule{150}{1}$

✠ Now let's convert cm into m

➨ 1 m = 100 cm

➨ 1 cm = 1/100 m

➨ 14400 / 100

➨ 144 m

${\green{\frak{Henceforth, \: 144 \: m \: is \: final \: result \: of \: the \: question}}}$