Question

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

Answer 1

Hint: Consider the car in the shape of a cuboid and find the total surface area of this cuboid assuming 4 m as its length (l), 3 m as the breadth (b), and 2.5 m as the height (h). Now, subtract the area of the base, whose dimensions are $l\times b$, from the total surface area to get the answer.

Complete step-by-step solution:
Here, we have been given a car which is to be covered with tarpaulin. We have to determine the area of tarpaulin required to cover the car if its height is 2.5 m and base dimensions are $4m\times 3m$.
Now, here we have to consider that the car is cuboidal in shape. Therefore, we have

In the above figure, we have assumed l, b, ‘h’ as the length, breadth, height of the car respectively. Now, the total area of tarpaulin that will be required to cover the car will be the sum of the lateral surface area of the cuboid and the area of the top. In other words, it can be said that the area required will be the difference between the total surface area of the cuboid and the area of its bottom. So, we have.
For the tarpaulin,
l = 4 m
b = 3 m
h = 2.5 m
We know that the total surface area of a cuboid is T.S.A = 2 (lb + bh + hl) and the area of the base is A = lb. So, taking their difference and substituting the values of l, b and h, we get
Area of tarpaulin required as
$\begin{align}
  & =2\left( lb+bh+hl \right)-lb \\
 & \Rightarrow lb+2\left( bh+hl \right) \\
 & \Rightarrow lb+2h\left( b+l \right) \\
 & \Rightarrow \left( 4\times 3 \right)+2\times 2.5\left( 4+3 \right) \\
 & \Rightarrow 12+\left( 5\times 7 \right) \\
 & \Rightarrow 12+35 \\
 & \Rightarrow 47{{m}^{2}} \\
\end{align}$
Hence, the area of tarpaulin needed to cover the car is $47{{m}^{2}}$.

Note: One may note that we do not have to consider the base area of the car because the base of the car is not getting covered. This information is provided in the question itself. You must remember the formula of total surface area and lateral surface area of some basic shapes like cube, cuboid, cone, etc. Note that we can also find the area of tarpaulin required by considering the sum of lateral surface area, i.e. 2h(l+b), and area of its top, i.e. lb.