2. The dimensions of a room are 16m x 14m x 10m. There are 4 windows of 1.3m x 1.4m and 2 doors of 2m x1m. What will be the whitewashing cost if the rate for whitewashing is Rs. 5/sq.m and rate of painting is Rs.8/sqm.
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Secondary School Math 5 points
The dimensions of a room are 16*14*10 metres. There are four windows of 1.3*1.4m and 2 doors of 2m*1m.what will be the cost of white washing the walls and painting the doors and windows, if the rate of painting is 8 rupees per metre square and whitewashing 5 rupees per metre square
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alokkashyap
alokkashyap Virtuoso
This is your solution
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sk940178 Virtuoso
The total cost of painting and whitewashing will be Rs. 3033.84.
Step-by-step explanation:
The room has dimensions of 16 m by 14 m by 10 m.
So, the area of the four walls (including the doors and windows) of the room will be = 2(L + W)H = 2(16 + 14) × 10 = 600 sq. meters.
Now the total area of four windows and two doors = 4(1.3 × 1.4) + 2(2 × 1) = 11.28 sq. meters.
So, the painting cost of the doors and windows at the rate of 8 Rs. per sq, meters will be (11.28 × 8) = 90.24 Rs.
Now, the area of the wall excluding the doors and windows is (600 - 11.28) = 588.72 sq. meters.
Hence, the cost of whitewashing the wall at a rate of 5 Rs. per sq. meters will be (588.72 × 5) = 2943.6 Rs.
Therefore, the total cost of painting and whitewashing will be (2943.6 + 90.24) = Rs. 3033.84. (Answer)
It seems minor mistake in the question,
Correct Question :
The dimensions of a room are 16 x 14 x 10 metres. There are four windows of 1.3 x 1.4m and 2 doors of 2m x 1 m.what will be the cost of white washing the walls and painting the doors and windows, if the rate of painting is 8 rupees per metre square and whitewashing 5 rupees per metre square.
Solution :
Given :
Dimensions of a Room,
- Length = 16 m
- Breadth = 14 m
- Height = 10 m.
Dimensions of 4 windows,
- Length = 1.3 m
- Breadth = 1.4 m
Dimensions of 2 Doors,
- Length = 2 m
- Breadth = 1 m
The rate for whitewashing is Rs. 5/sq.m
The rate for painting is Rs. 8/sq.m
To find :
- The total cost of whitewashing and painting =?
Step-by-step explanation :
Lateral Surface Area of Cuboid = Area of room's walls = 2 ( l + b) × h
Substituting the values in the above formula, we get,
= 2 ( 16 + 14) × 10
= 2 ( 30 ) × 10
= 2 × 30 × 10
= 600.
Therefore, the Area of it's walls = 600 m².
Now,
Area of one window = Area of rectangle = length x breadth.
Substituting the values in the above formula, we get,
= 1.3 × 1.4
= 1.82
Therefore, Area of one window = 1.82 m².
So,
Area of 4 windows = 4 × Area of one window
Substituting the values, we get,
= 4 × 1.82
= 7.28.
Therefore, Area of 4 windows = 7.28 m².
Now,
Area of one Door = Area of rectangle = length x breadth
Substituting the values in the above formula, we get,
= 2 × 1
= 2.
Therefore, Area of one Door = 2 m².
So,
Area of 2 Doors = 2 × Area of one Door
Substituting the values, we get,
= 2 × 2
= 4.
Therefore, Area of 2 Doors = 4 m².
Now,
Total Area of the 4 windows and 2 Doors = Area of 4 windows + Area of 2 Doors.
Substituting the values, we get,
= 7.28 + 4
= 11.28
Therefore, Total Area of the 4 windows and 2 Doors = 11.28 m²
Now,
Area to be whitewashing = Area of the walls - Total Area of the 4 windows and 2 Doors.
Substituting the values, we get,
= 600 - 11.28
= 588.72
Therefore, Area to be whitewashing = 588.72 m².
As We know that,
The rate for whitewashing is Rs. 5/sq.m
So,
Total cost of whitewashing = The rate for whitewashing × Area to be whitewashing.
Substituting the values, we get,
= 5 × 588.72
= 2943.6
Therefore, Total cost of whitewashing = ₹ 2943.6
Now,
Rate of the painting = 8 m². [Given]
So,
Total cost of painting = Rate of the painting × total area of 4 windows and 2 doors.
Substituting the values, we get,
= 8 × 11.28
= 90.24
Therefore, the total cost of painting = ₹ 90.24
Now,
Total cost of whitewashing and painting = total cost of whitewashing + total cost of painting.
Substituting the values, we get,
= 2943.6 + 90.24
= 3033.84
Therefore, Total cost of whitewashing and painting = ₹ 3033.84