Question

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Q. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of Rs.7.50 per sq.m. Also, find the cost of painting floor at ₹10 per m.

Answer 1

Answer:

${\textsf{\textbf{Given}}}$

• Length of room = 5 m
• Breadth of room = 4 m
• Height of room = 3 m
• Cost of white washing per m = ₹7.50
• Cost of painting = ₹10

${ \textsf{ \textbf{To \: Find}}}$

• Cost of ceiling
• Cost of painting floor at ₹10 per m

${ \textsf{\textbf{Solution}}}$

At first we will find the area of room

Lateral Surface area of room = 2h(l + b)

• H is the Height
• L is the Length
• B is the Breadth

LSA = 2 × 3(5 + 4)

LSA = 6(5 + 4)

LSA = 6(9)

LSA = 54 m²

Now,

Area of ceiling = Length × Breadth

Area = 5 × 4

Area = 20 m²

Now,

Total area = Area of ceiling + Lateral Surface area of room

Total area = 20 + 54

Total area = 74 m²

Now,

Cost of white washing = Total area to be white washed × Cost of white washing 1 m²

Cost of white washing = 74 × 7.5

Cost of white washing = ₹555

Cost of white washing is ₹555.

Now,

Diagram of Floor

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 5 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 4 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Cost of painting floor = Area of floor × Cost of painting 1 m²

Cost of painting = (5 × 4) × 10

Cost of painting = 20 × 10

Cost of painting = ₹200

Cost of painting is ₹200

Answer 2

Required Answer :

Given :

• Length of the room = 5 m

• Breadth of the room = 4 m

• Height of the room = 3 m

• Cost of white washing the wall per m = ₹ 7.50

• Cost of painting the floor per m = ₹ 10

To Find :

• The cost of ceiling

• The cost of painting the floor at ₹ 10 per m

Formula Used :

• Lateral surface area of the room = 2h × ( Length + Breadth )

• Area of ceiling = Length × Breadth

• Total Area of the room = Area of ceiling + Lateral surface area of the room

• Cost of white washing the wall = Total Area to be washed × Cost of white washing 1 m²

• Cost of painting the floor = Area of the floor × Cost of painting 1 m²

Solution :

First of all, we need to find out the area of the room, so let's do it!

Remember,

• H = Height

• L = Length

• B = Breadth

Lateral surface area of the room = 2h × ( Length + Breadth )

Lateral surface area of the room = 2 × 3 ( 5 + 4 )

Lateral surface area of the room = 6 × 9

Lateral surface area of the room = 54 m²

Now, let's find out the area of ceiling!

Area of ceiling = Length × Breadth

Area of ceiling = 5 × 4

Area of ceiling = 20 m²

Now, let's calculate the total area!

Total Area of the room = Area of ceiling + Lateral surface area of the room

Total Area of the room = 20 + 54

Total Area of the room = 74 m²

Now, let's calculate the cost of white washing the wall!

Cost of white washing the wall = Total Area to be washed × Cost of white washing 1 m²

Cost of white washing the wall = 74 × 7.5

Cost of white washing the wall = ₹ 555

∴ Cost of white washing the wall is ₹ 555

Now, let's find out the cost of painting the floor!

Cost of painting the floor = Area of the floor × Cost of painting 1 m²

Cost of painting the floor = ( 5 × 4 ) × 10

Cost of painting the floor = 20 × 10

Cost of painting the floor = ₹ 200

∴ Cost of painting the floor is ₹ 200

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