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An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.?
Most Upvoted Answer
An open box is made of wood 3cm thick. Its external length, breadth, h...
Solution:
Given:
External dimensions of the open box:
Length = 1.48 m
Breadth = 1.16 m
Height = 8.3 dm
Thickness of the wood = 3 cm
To find:
The cost of painting the inner surface of the box at a rate of 50 rupees per square meter.
Step 1: Convert the dimensions to the same unit
Since the thickness of the wood is given in centimeters, we need to convert the other dimensions to centimeters as well.
Length = 1.48 m = 148 cm
Breadth = 1.16 m = 116 cm
Height = 8.3 dm = 83 cm
Step 2: Calculate the inner dimensions of the box
To find the inner dimensions of the box, we need to subtract twice the thickness of the wood from each external dimension.
Inner length = External length - 2 * Thickness of wood
= 148 cm - 2 * 3 cm
= 148 cm - 6 cm
= 142 cm
Inner breadth = External breadth - 2 * Thickness of wood
= 116 cm - 2 * 3 cm
= 116 cm - 6 cm
= 110 cm
Inner height = External height - 2 * Thickness of wood
= 83 cm - 2 * 3 cm
= 83 cm - 6 cm
= 77 cm
Step 3: Calculate the surface area to be painted
The inner surface of the box consists of the inner sides and the bottom. The surface area to be painted can be calculated by finding the areas of these surfaces and adding them together.
Area of the inner sides = 2 * (Inner length * Inner height + Inner breadth * Inner height)
= 2 * (142 cm * 77 cm + 110 cm * 77 cm)
= 2 * (10934 cm^2 + 8470 cm^2)
= 2 * 19404 cm^2
= 38808 cm^2
Area of the bottom = Inner length * Inner breadth
= 142 cm * 110 cm
= 15620 cm^2
Total surface area to be painted = Area of the inner sides + Area of the bottom
= 38808 cm^2 + 15620 cm^2
= 54428 cm^2
Step 4: Convert the surface area to square meters
To calculate the cost of painting, we need to convert the surface area from square centimeters to square meters.
Surface area in square meters = Surface area in square centimeters / 10000
= 54428 cm^2 / 10000
= 5.4428 m^2
Step 5: Calculate the cost of painting
The cost of painting the inner surface of the box can be calculated by multiplying the surface area in square meters by the rate per square meter.
Cost of painting = Surface area in square meters * Rate per square meter
= 5.4428 m^2 * 50 rupees/m^2
= 272.14 rupees
Therefore, the cost of painting the inner surface of the box at a rate of 50 rupees per square meter is 272.14 rupees.
Given:
External dimensions of the open box:
Length = 1.48 m
Breadth = 1.16 m
Height = 8.3 dm
Thickness of the wood = 3 cm
To find:
The cost of painting the inner surface of the box at a rate of 50 rupees per square meter.
Step 1: Convert the dimensions to the same unit
Since the thickness of the wood is given in centimeters, we need to convert the other dimensions to centimeters as well.
Length = 1.48 m = 148 cm
Breadth = 1.16 m = 116 cm
Height = 8.3 dm = 83 cm
Step 2: Calculate the inner dimensions of the box
To find the inner dimensions of the box, we need to subtract twice the thickness of the wood from each external dimension.
Inner length = External length - 2 * Thickness of wood
= 148 cm - 2 * 3 cm
= 148 cm - 6 cm
= 142 cm
Inner breadth = External breadth - 2 * Thickness of wood
= 116 cm - 2 * 3 cm
= 116 cm - 6 cm
= 110 cm
Inner height = External height - 2 * Thickness of wood
= 83 cm - 2 * 3 cm
= 83 cm - 6 cm
= 77 cm
Step 3: Calculate the surface area to be painted
The inner surface of the box consists of the inner sides and the bottom. The surface area to be painted can be calculated by finding the areas of these surfaces and adding them together.
Area of the inner sides = 2 * (Inner length * Inner height + Inner breadth * Inner height)
= 2 * (142 cm * 77 cm + 110 cm * 77 cm)
= 2 * (10934 cm^2 + 8470 cm^2)
= 2 * 19404 cm^2
= 38808 cm^2
Area of the bottom = Inner length * Inner breadth
= 142 cm * 110 cm
= 15620 cm^2
Total surface area to be painted = Area of the inner sides + Area of the bottom
= 38808 cm^2 + 15620 cm^2
= 54428 cm^2
Step 4: Convert the surface area to square meters
To calculate the cost of painting, we need to convert the surface area from square centimeters to square meters.
Surface area in square meters = Surface area in square centimeters / 10000
= 54428 cm^2 / 10000
= 5.4428 m^2
Step 5: Calculate the cost of painting
The cost of painting the inner surface of the box can be calculated by multiplying the surface area in square meters by the rate per square meter.
Cost of painting = Surface area in square meters * Rate per square meter
= 5.4428 m^2 * 50 rupees/m^2
= 272.14 rupees
Therefore, the cost of painting the inner surface of the box at a rate of 50 rupees per square meter is 272.14 rupees.
Community Answer
An open box is made of wood 3cm thick. Its external length, breadth, h...
Solution: -
External length=1.48m
External breadth=1.16dm=11.6 m [1dm=10m]
External height=8.3dm=83m
Thickness of wood is 3cm=0.03m [1cm=0.01m]
Subtracting 3+3=6cm from external length, breadth and height respectively: -
1.48m-0.03m=1.45m
11.60m-0.03m=11.57m
83.00m-0.03m=82.97m
area of 4 walls and bottom
=[{2(length*height) +2(breadth*height)} +{length*breadth}]
= {[2(1.48m*83m) +2(11.6m*83m)} + {1.48m*11.6m}]
= [{245.68m^2+1,925.6m^2m} {17.168m^2}]
= [2,171.28m^2+17.168m^2]
=2,188.448m^2 =2,188.5m^2 =2,189m^2
Cost of painting 1m^2=₹50
Cost of painting 2,189m^2=₹2,189*50=₹1,09,450
Answer: - Cost of painting inner surface of box will be ₹109450.
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An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.?
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An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.?.
An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An open box is made of wood 3cm thick. Its external length, breadth, height are 1.48m,1.16 and 8.3dm. Find the cost of painting the inner surface of 50 rupee per m^2.?.
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