Question

20. A room is 8.5 m long. 6.5 m broad and 3.4 m high. It has two doors, each measuring
(15 m by 1 m) and two windows, each measuring (2 m by 1 m). Find the cost of painting its
four walls at 160 per m².​

Answer 1

$\huge{\underline{\boxed{\sf Corrrect\: Question}}}$

A room is 8.5 m long. 6.5 m broad and 3.4 m high. It has two doors, each measuring (1.5 m by 1 m) and two windows, each measuring (2 m by 1 m). Find the cost of painting its four walls at 160 per m².

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have given the dimension of a room and its two windows and doors and we have to find the cost of painting the four walls at the rate of 160/m² (without including doors and windows).

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, we simply apply the formula of curved surface area for four walls then substituting given values in it we will got the area of four walls then finding the area of two doors and two windows then we simply substract the area of doors and windows from the area of four walls and we will got the area of wall which is to be painted. Then, for finding the cost we will multiply it from given rate of painting (Rs.60) which is our required answer.

$\huge{\underline{\boxed{\sf AnSwer}}}$

____________________________

Given:-

• Room is 8.5m long, 6.5m broad and 3.4m high
• Measures of two doors = 15m by 1m
• Measures of two windows = 2m by 1m

Find:-

• Cost of painting its four walls at the rate of 160 per m²

Solution:-

Here, we know that

$\\ :\implies \: \: \: \: \underline{\boxed{\sf Area \: of \: four \: walls = 2(l + b)h}}$

$\sf where \small{\begin{cases} \sf l = 8.5m \\\sf b = 6.5m \\ \sf h = 3.4m\end{cases}}$

✟ Substituting these values:

$\dashrightarrow\sf Area_{four \: walls} = 2(l + b)h$

$\dashrightarrow\sf Area_{four \: walls} = 2(8.5 + 6.5)3.4$

$\dashrightarrow\sf Area_{four \: walls} = 2(15)3.4$

$\dashrightarrow\sf Area_{four \: walls} = 2 \times 15 \times 3.4$

$\dashrightarrow\sf Area_{four \: walls} = 30 \times 3.4$

$\dashrightarrow\sf Area_{four \: walls} = 102 {m}^{2}$

$\boxed{\sf Area_{four \: walls} = 102 {m}^{2}}$

$\qquad$_______________________

$\underline{\red{\textsf{For Doors:}}}$

we, know that

$\\ :\implies \: \: \: \: \underline{\boxed{\sf Area \: of \: door = l \times b}}$

$\sf where \small{\begin{cases} \sf l = 1.5m \\\sf b = 1m \end{cases}}$

✙ Substituting these values:

$:\to\sf Area_{door} = l \times b$

$:\to\sf Area_{door} = 1.5\times 1$

$:\to\sf Area_{door} = 1.5 {m}^{2}$

➩ Area of 2 doors = 2×Area if 1 door

➩ Area of 2 doors = 2×1.5 = 3m²

$\qquad$_______________________

$\underline{\red{\textsf{For Windows:}}}$

we, know that

$\\ :\implies \: \: \: \: \underline{\boxed{\sf Area \: of \: window= l \times b}}$

$\sf where \small{\begin{cases} \sf l = 2m \\\sf b = 1m \end{cases}}$

✝ Substituting these values:

$\implies\sf Area_{window} = l \times b$

$\implies\sf Area_{window} = 2 \times 1$

$\implies\sf Area_{window} = 2 {m}^{2}$

➫ Area of 2 windows = 2×Area of 1 window

➫ Area of 2 windows = 2×2 = 4m²

$\qquad$_______________________

Now, Area if wall to be painted

➳ Area to be painted = Area of 4 walls - Area of 2 doors - Area of 2 windows

➳ Area to be painted = 102 - 3 - 4

➳ Area to be painted = 102 - 7

➳ Area to be painted = 95m²

$\qquad$_______________________

Now,

❍ Cost of painting 1m² = Rs. 160

❍ Cost of painting 95m² = 160×95 = Rs. 15200

$\underline{\boxed{\sf \therefore Cost\:of\: painting\:four\:walls\:is\:Rs.15200}}$

Answer 2

Answer:

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Step-by-step explanation:

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