Question

21. The walls and ceiling of a room 7 m long, 5 m wide and 3.5 m high are covered with paper 6 dm wide.
Find the length of paper required, if no length less than a metre can be bought.​

Answer 1

Given :

• length : 7m
• breadth : 5m
• height : 3.5 m

To Find :

• Paper required to cover => ceiling and 4 walls

Formula :

$\boxed{\rm{ 2(l + b) \times h \times l \times b}}$

Here we are using the formula of Total surface area but only for 5 sides i.e excluding the sixth side being the floor. After finding the area ; we can calculate the length of paper required.

Putting up the formula :

Area :

$\tt{ 2 ( 7 + 5) \times 3.5 + 7 \times 5}$

$\tt{ 24 \times 3.5 + 7 \times 5}$

$\tt{ 24 \times 3.5 + 35}$

$\large{\boxed{\tt{ {119m}^{2}}}}$

Length of paper :

Area of 4 walls + Area of ceiling

Width : 0.6 m

Area = length × breadth

119 = length × 0.6

length = 119 ÷ 0.6

length = 198.33m

So , the length =>

198.33m

Answer 2

$\blue{\bold{\underline{\underline{Question}}}}$

The walls and ceiling of a room 7 m long, 5 m wide and 3.5 m high are covered with paper 6 dm wide.Find the length of paper required, if no length less than a metre can be bought.

$\blue{\bold{\underline{\underline{Answer}}}}$

The length of a paper required is 198.33 meters.

$\blue{\bold{\underline{\underline{Explanation}}}}$

given

Length of room = 7 m

Width of room = 5 m

Height of room = 3.5 m

So, Area of 4 walls and the ceiling would be 2(l+b) ×h+l×b

=2(7+5) ×3.5+7×5

=84+35

=119m^2

If the width of paper = 6 dm = 0.6 m

So, Area of 4 walls + Area of ceiling = Area of paper

119=0.6×l

119/0.6=l

l=198.33

Hence, the length of a paper required is 198.33 meters.