Question

$\huge\bf\color{teal}{Question༉}$

Praveen 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 2.5m, with base dimensions 4m×3m?​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Measure of length of the shelter = 4 metres.
• Measure of breadth of the shelter = 3 metres.
• Measure of height of the shelter = 2.5 metres.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The amount of tarpaulin that would be required to make the shelter.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{TSA}_{(Cuboid)}=2(lb+bh+hl)\:sq.units}}}$

$\underline{\boxed{\sf{{Area}_{(Rectangle)}=lb\:sq.units}}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{l=length}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{b=breadth}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{h=height}}$

${\underline{\underline{\bf{Solution:}}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎We need to find the amount of tarpaulin required to make the shelter for Praveen's car. We know that the Tarpaulin covers the top and the lateral sides (i.e, the 5 sides excluding the base). So, tha answer can be found by subtracting the area of base from the total surface area of the shelter.

TSA of shelter:

$\implies{\sf{2(lb+bh+hl\:sq.units}}$

$\implies{\sf{2\times (4\times 3+3\times 2.5+2.5\times 4)}}$

$\implies{\sf{2\times (12+7.5+10)}}$

$\implies{\sf{2\times (19.5+10)}}$

$\implies{\sf{2\times 29.5}}$

$\implies{\underline{\underline{\sf{59\:{m}^{2}}}}}$

Area of base:

$\implies{\sf{lb\:sq.units}}$

$\implies{\sf{4\times 3}}$

$\implies{\underline{\underline{\sf{12\:{m}^{2}}}}}$

★ Amount of Tarpaulin required:

$\rightarrow{\sf{TSA\:of\: shelter-Area\:of\:base}}$

$\rightarrow{\sf{59-12}}$

$\rightarrow{\sf{\red{\underline{\underline{47\:{m}^{2}}}}}}$

${\underline{\underline{\bf{Required\: answer:}}}}$

• 47 m² of Tarpaulin is required to make the shelter for Praveen's car.

_____________________________________________

${\underline{\underline{\bf{Alternative\:method:}}}}$

Above, we've found the answer by subtracting the area of base from the total surface area. We can also find the answer by summing up the area of top and the lateral surface area.

$\rightarrow{\sf{Area\:of\:top+LSA\:of\:shelter}}$

$\rightarrow{\sf{[lb]+[2h(l+b)]}}$

$\rightarrow{\sf{[4\times 3]+[2\times 2.5\times (4+3)]}}$

$\rightarrow{\sf{12+[5\times7]}}$

$\rightarrow{\sf{12+35}}$

$\rightarrow{\sf{\red{\underline{\underline{47\:{m}^{2}}}}}}$

_____________________________________________

Answer 2

$\huge\colorbox{pink}{Answer ✔}$

Let l, b and h be the length, breadth and height of the shelter.

Given:

l = 4m

b = 3m

h = 2.5m

Tarpaulin will be required for the top and four wall sides of the shelter.

Using formula, Area of tarpaulin required = 2(lh + bh)+lb

Put the values of l, b and h, we get

= [2(4 × 2.5 + 3 × 2.5) + 4 × 3] m²

= [2(10 + 7.5) + 12]m²

= 47 m²

Therefore, 47 m² tarpaulin will be required

Hope it helps you ☺️✔️

_____________________________________________