Question

a conference hall is 14m long , 8 m wide, and 4m high. there are four Windows and one door in it. the door measures 1m by 2m and each window measures 1m by 1.5 m. what will be the cost of painting the hall if 1 litre costs rupees 225?​

Answer 1

Correct Question :

Aconference hall is 14m long , 8 m wide, and 4m high. there are four Windows and one door in it. the door measures 1m by 2m and each window measures 1m by 1.5 m. 1 litre will be enough for covering 18m^2. Find the cost of painting the hall if 1 litre costs rupees 225?

Solution :

Here,

$\diamond \: \mathfrak Length = 14 \: m$

$\diamond \: \mathfrak Breadth = 8 \: m$

$\diamond \: \mathfrak Height= 4 \: m$

Area of 4 walls :

$\sf \: Area = 2(l + b)h$

$\hookrightarrow \sf \: 2(14 + 8)4$

$\hookrightarrow \sf \: 2(22)4$

$\hookrightarrow \sf \: 176 {m}^{2}$

Area of 4 windows :

$\sf\: Area \: of \: 1 \: door = 2 {m}^{2}$

$\sf \: Area \: of \: 1 \: window = 1.5 {m}^{2}$

$\therefore \sf \: Area \: of \: 4 \: windows = 4 \times 1.5m$

$\hookrightarrow \sf \: 6 {m}^{2}$

Area of 4 walls to be painted :

[Area of 4 walls - Area of windows + doors]

$\hookrightarrow \sf \: 176 - (2 + 6)$

$\hookrightarrow \sf \: 176 - 8$

$\hookrightarrow \sf \: 168 {m}^{2}$

Litres of Paint required :

$\star \tt \: 18 {m}^{2} = 1 \: litre$

$\hookrightarrow \sf \: 168 {m}^{2} = \dfrac{168}{18}$

$\hookrightarrow \sf \: 168 {m}^{2} = \dfrac{28}{3} litre \: = 9 \dfrac{1}{3} litre$

$\star \tt \: \: Cost \: of \: 1 \: litre = Rs \: 225$

$\hookrightarrow \sf \: \dfrac{28}{3} \: litre = \cancel \dfrac{225 \times 28}{3}$

$\hookrightarrow \sf \: \dfrac{28}{3} \: litre = Rs \: 2100$

Cost of painting the hall = Rs 2100

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\purple{ANSWER\::}}}}}}$

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

A conference hall is 14m long, 8m wide and 4m high.There are foue windows and one door in it. the door measures 1m by 2m and each window measures 1m by 1.5m.1 litre will be enough for covering 18m^2.

$\bf{\Large{\underline{\bf{To\:Find\::}}}}$

The cost of painting the hall if 1 litre cost Rs.225.

$\bf{\Large{\underline{\boxed{\rm{\green{Explanation\::}}}}}}$

$\bf{We\:have\begin{cases}\rm{The\:length\:of\:hall\:(L)\:=\:14m}\\ \sf{The\:breadth\:of\:hall\:(B)\:=\:8m}\\ \sf{The\:height\:of\:hall\:(H)\:=\:4m}\end{cases}}$

We know that area of four wall : $\rm{\red{2(L+B)H}}$

$\longmapsto\rm{Area\:of\:hall\:=\:[2(14+8)4]m^{2} }$

$\longmapsto\rm{Area\:of\:hall\:=\:[2(22)]4m^{2} }$

$\longmapsto\rm{Area\:of\:hall\:=\:(8*22)m^{2} }$

$\longmapsto\rm{Area\:of\:hall\:=\:\sf{\red{176m^{2}}} }$

• $\bf{\Large{\underline{\rm{\orange{Area\:of\:4\:windows\::}}}}}$

We have,

4 windows & 1 door :

Length of door = 1m

Breadth of door = 2m

$\rm{\large{\boxed{\sf{\pink{Area\:of\:the\:door\:=\:(1*2)m^{2} =2m^{2} }}}}}}$

Length of window = 1m

Breadth of window = 1.5m

$\rm{\large{\boxed{\sf{\pink{Area\:of\:the\:window\:=\:(1*1.5)m^{2} =1.5m^{2} }}}}}}$

So,

→ 4 windows = (4 × 1.5)m²

→ 4 windows = 6m²

$\bf{\Large{\boxed{\rm{\red{Required\:area\:for\:painting\::}}}}}$

$\mapsto\rm{Area\:of\:foor\:wall\:-\:Area\:of\:door\:-\:Area\:of\:4\:window}$

$\mapsto\rm{176m^{2}\:-\:2m^{2}\:-\:6m^{2}}$

$\mapsto\rm{176m^{2}\:-\:8m^{2}}$

$\mapsto\rm{\red{{168m^{2}}}}$

_________________________________________________

We have,

1 litre is enough for covering 18m².

So,

The cost of painting = 168m²

∴ Litres = $\rm{\cancel{\frac{168}{18} l}}$

→ Litres = 9.33 litres

Now,

⇒ The cost of 1 litre = Rs.225

⇒ The cost of 9.33 litres = Rs.(9.33 × 225)

⇒ The cost of 9.33 litres = Rs.2099.9

Thus,

$\rm{\large{\boxed{\sf{\red{The\:total\:cost\:of\:painting\:the\:hall\:=Rs.2100}}}}}}}$  [approx]