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

## 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.