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The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid?
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The diameter of a cuboid are in the ratio of 3:4:5 and total surface a...
Is it diameter or dimension? How will a cuboid have diameter?I think the qn is to find dimensions of cuboid.
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The diameter of a cuboid are in the ratio of 3:4:5 and total surface a...
Given:
The ratio of the diameters of a cuboid is 3:4:5.
Total surface area = 188 cm².
To find:
The diameter of the cuboid.
Solution:
Step 1: Understand the problem:
We are given the ratio of the diameters and the total surface area of a cuboid. We need to find the diameter of the cuboid.
Step 2: Identify the formula:
The formula to calculate the total surface area of a cuboid is:
Total Surface Area = 2(lw + lh + wh)
Step 3: Set up the equation:
Let the diameters of the cuboid be 3x, 4x, and 5x.
The formula for the total surface area can be rewritten as:
188 = 2(3x * 4x + 3x * 5x + 4x * 5x)
Step 4: Simplify the equation:
188 = 2(12x² + 15x² + 20x²)
188 = 2(47x²)
188 = 94x²
x² = 188/94
x² = 2
x = √2
Therefore, the diameter of the cuboid is:
3x = 3√2
4x = 4√2
5x = 5√2
Step 5: Calculate the diameter:
To find the actual diameter, we need to find the value of √2.
Using a calculator, we find that √2 is approximately 1.414.
Therefore, the diameter of the cuboid is:
3(1.414) = 4.242
4(1.414) = 5.656
5(1.414) = 7.071
Step 6: Answer:
The diameter of the cuboid is approximately 4.242 cm, 5.656 cm, and 7.071 cm.
The ratio of the diameters of a cuboid is 3:4:5.
Total surface area = 188 cm².
To find:
The diameter of the cuboid.
Solution:
Step 1: Understand the problem:
We are given the ratio of the diameters and the total surface area of a cuboid. We need to find the diameter of the cuboid.
Step 2: Identify the formula:
The formula to calculate the total surface area of a cuboid is:
Total Surface Area = 2(lw + lh + wh)
Step 3: Set up the equation:
Let the diameters of the cuboid be 3x, 4x, and 5x.
The formula for the total surface area can be rewritten as:
188 = 2(3x * 4x + 3x * 5x + 4x * 5x)
Step 4: Simplify the equation:
188 = 2(12x² + 15x² + 20x²)
188 = 2(47x²)
188 = 94x²
x² = 188/94
x² = 2
x = √2
Therefore, the diameter of the cuboid is:
3x = 3√2
4x = 4√2
5x = 5√2
Step 5: Calculate the diameter:
To find the actual diameter, we need to find the value of √2.
Using a calculator, we find that √2 is approximately 1.414.
Therefore, the diameter of the cuboid is:
3(1.414) = 4.242
4(1.414) = 5.656
5(1.414) = 7.071
Step 6: Answer:
The diameter of the cuboid is approximately 4.242 cm, 5.656 cm, and 7.071 cm.
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The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid?
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The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid? 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 diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid?.
The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid? 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 diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diameter of a cuboid are in the ratio of 3:4:5 and total surface area is 188 cm . find the diameter of cuboid?.
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