Ex.11.3 Q2 Mensuration Solution - NCERT Maths Class 8

Go back to  'Ex.11.3'

Question

A suitcase with measures \(80\,\rm{ cm} × 48\, \rm{cm} × 24\,\rm{ cm}\) is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width \(96\,\rm{cm}\) is required to cover \(100\) such suitcases?

 Video Solution
Mensuration
Ex 11.3 | Question 2

Text Solution

What is Known?

Number of suitcases to be covered and dimensions of each suitcase.

What is unknown?

Required length of tarpaulin cloth cover suitcase

Reasoning:

Find the surface area of a suitcase.

Steps:

Let the length of the tarpaulin cloth \(= l \,\rm{cm}\)

Total surface of the suitcase

\[\begin{align} &= 2[(80\! \times\! 48) \!+\! (48\! \times\! 24) \!+\!(24 \!\times \!80)]\,{\rm{cm}^2}\\&= 2[3840 + 1152 + 1920]\,{\rm{c}}{{\rm{m}}^2}\\ &= 13824 \,\rm{m^2} \end{align}\]

Total surface area of \(100\) suitcases

\[\begin{align} &= 100 \times 13824\,{{\rm{m}}^2}\\&= 1382400\,\,{\rm{cm}^2}\end{align}\]

Required Tarpaulin cloth

\[= {\rm{Length\! \times\! Breadth}}\]

\(1382400\,{\rm{c}}{{\rm{m}}^2} = l \times 96\,{\rm{cm}}\) 

\[\begin{align}l& = \frac{{1382400}}{{96}}\,\,{\rm{cm}}\\&= 14400\,\,{\rm{cm}}\\l& = 144\,\rm{m}\end{align}\]

Thus, \(144\;\rm{ m}\) of tarpaulin cloth is required to cover \(100\) suitcases.

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school