Question

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

Answer 1

Answer :

198.33 m.

Step-by-step explanation:

Given :

• Length = 7m
• Breadth = 5m
• Height = 3.5 m

To Find :

• Paper required to cover ceiling and 4 walls

Solution :

Here, we will be 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. Formula :

$\longrightarrow \: \boxed{\bf{ 2(l + b) \times h \times l \times b}} \: \bigstar$

Substituting the values, for finding area :

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

$\implies\sf{ 2 ( 12) \times 3.5 + 7 \times 5}$

$\implies\sf{ 24 \times 3.5 + 7 \times 5}$

$\implies\sf{ 24 \times 3.5 + 35}$

$\implies{\boxed{\bf{ {119 \: m}^{2}}}} \: \:$

So, the area is 119 m².

Now, let's find the length of paper.

★ Length of paper : Area of 4 walls + Area of ceiling

We have,

• Width = 0.6 m

$\sf \longrightarrow \: Area =Length \times Breadth$

$\sf \longrightarrow \: 119 =Length \times 0.6$

$\sf \longrightarrow \: Length = \dfrac{119}{ 0.6}$

$\sf \pink{\longrightarrow \: \boxed{ \bf \: Length = 198.33 \: m}} \: \bigstar$

Hence, the length is 198.33 m.