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The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension?
Most Upvoted Answer
The dimension of a cuboid are in the ratio 5:4:3 and its total surface...
Let dimension of cuboid be 5x, 4x and 3x respectively.
Total surface area of cuboid = 2(lb+bh+hl)
=>846= 2{(5x*4x)+(4x*3x)+(3x*5x)
=>846=2(20x^2+12x^2+15x^2)
=>846=2*47x^2
=>846/2*47=x^2
=>9=x^2
=>√9=x
=>x=3cm
so l=5x =5*3 = 15
b=4x=4*3=12
h= 3x= 3*3=9.
If this is right answer then upvote my answer.
Total surface area of cuboid = 2(lb+bh+hl)
=>846= 2{(5x*4x)+(4x*3x)+(3x*5x)
=>846=2(20x^2+12x^2+15x^2)
=>846=2*47x^2
=>846/2*47=x^2
=>9=x^2
=>√9=x
=>x=3cm
so l=5x =5*3 = 15
b=4x=4*3=12
h= 3x= 3*3=9.
If this is right answer then upvote my answer.
Community Answer
The dimension of a cuboid are in the ratio 5:4:3 and its total surface...
Given:
- The dimension of the cuboid is in the ratio 5:4:3.
- The total surface area of the cuboid is 846 cm².
To Find:
The dimensions of the cuboid.
Solution:
Step 1: Establishing the Ratio:
Let the dimensions of the cuboid be 5x, 4x, and 3x, where x is a constant.
Step 2: Determining the Surface Area:
The total surface area of a cuboid is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the given dimensions, we get:
2(5x)(4x) + 2(5x)(3x) + 2(4x)(3x) = 846
Simplifying the equation, we have:
40x² + 30x² + 24x² = 846
94x² = 846
x² = 9
x = 3 or -3
Since the dimensions cannot be negative, x = 3.
Step 3: Finding the Dimensions:
Substituting the value of x in the ratio, we get:
Length = 5x = 5 * 3 = 15 cm
Breadth = 4x = 4 * 3 = 12 cm
Height = 3x = 3 * 3 = 9 cm
Therefore, the dimensions of the cuboid are:
Length = 15 cm
Breadth = 12 cm
Height = 9 cm
Conclusion:
The dimensions of the cuboid are 15 cm, 12 cm, and 9 cm.
- The dimension of the cuboid is in the ratio 5:4:3.
- The total surface area of the cuboid is 846 cm².
To Find:
The dimensions of the cuboid.
Solution:
Step 1: Establishing the Ratio:
Let the dimensions of the cuboid be 5x, 4x, and 3x, where x is a constant.
Step 2: Determining the Surface Area:
The total surface area of a cuboid is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the given dimensions, we get:
2(5x)(4x) + 2(5x)(3x) + 2(4x)(3x) = 846
Simplifying the equation, we have:
40x² + 30x² + 24x² = 846
94x² = 846
x² = 9
x = 3 or -3
Since the dimensions cannot be negative, x = 3.
Step 3: Finding the Dimensions:
Substituting the value of x in the ratio, we get:
Length = 5x = 5 * 3 = 15 cm
Breadth = 4x = 4 * 3 = 12 cm
Height = 3x = 3 * 3 = 9 cm
Therefore, the dimensions of the cuboid are:
Length = 15 cm
Breadth = 12 cm
Height = 9 cm
Conclusion:
The dimensions of the cuboid are 15 cm, 12 cm, and 9 cm.
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The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension?
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The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension? 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 The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension?.
The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension? 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 The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimension of a cuboid are in the ratio 5:4:3 and its total surface area is 846cm? Find its dimension?.
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