Ex.13.1 Q8 Surface Areas and Volumes - NCERT Maths Class 9

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Question

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height \(\begin{align}2.5 \rm{m} \end{align}\), with base dimensions \(\begin{align}4\,\rm{m} \times 3\,\rm{m}?\end{align}\)

Text Solution

Reasoning:

The surface area of the cuboid is the sum of the surface area of the faces. Since Parveen wanted to make a cuboid with \(5\) outer faces covered with tarpaulin that covers all the four side and the top.

What is the known?

Measurements of the shelter needed is given.

What is the unknown?

Area of the tarpaulin required to make the shelter.

Steps:

\[\begin{align}\text{length(l)} &= 4\rm{m} \\\text{breadth(b)} &= 3\rm{m}\\\text{height(h) }&= 2.5\rm{m} \end{align}\]

Total surface area with five faces 

\[\begin{align} &= lb + 2(bh + hl) \\& = 4 \times 3 + 2(3 \times 2.5 + 2.5 \times 4)\\ &= 12 + 2[7.5{\rm{ + }}10]\\ &= 47\,\rm{cm^2} \end{align}\]

Hence\(\begin{align}\,47\,\rm{cm^2} \end{align}\) of tarpaulin will be required.

  
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