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A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is?
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A cuboid has a total surface area of 384 cm^2.The sum of the squares o...
Calculating the Length of the Cuboid
1. Given Information:
- Total surface area of the cuboid = 384 cm^2
- Sum of the squares of its length, breadth, and height = 192 cm^2
2. Surface Area of a Cuboid:
The total surface area of a cuboid is given by the formula:
Surface Area = 2(lb + bh + hl), where l = length, b = breadth, h = height.
3. Equation 1:
From the given information, we have:
2(lb + bh + hl) = 384
4. Equation 2:
The sum of the squares of length, breadth, and height is given by:
l^2 + b^2 + h^2 = 192
5. Substitute and Simplify:
- Using Equation 1 and Equation 2, we can substitute the values to get:
2(lb + bh + hl) = 384
l^2 + b^2 + h^2 = 192
6. Find the Length:
- To find the length, we need to solve these equations simultaneously to get the value of l.
7. Conclusion:
- By solving the equations, we can find the length of the cuboid.
By following these steps and solving the equations accurately, you can determine the length of the cuboid using the given information about its total surface area and the sum of the squares of its dimensions.
1. Given Information:
- Total surface area of the cuboid = 384 cm^2
- Sum of the squares of its length, breadth, and height = 192 cm^2
2. Surface Area of a Cuboid:
The total surface area of a cuboid is given by the formula:
Surface Area = 2(lb + bh + hl), where l = length, b = breadth, h = height.
3. Equation 1:
From the given information, we have:
2(lb + bh + hl) = 384
4. Equation 2:
The sum of the squares of length, breadth, and height is given by:
l^2 + b^2 + h^2 = 192
5. Substitute and Simplify:
- Using Equation 1 and Equation 2, we can substitute the values to get:
2(lb + bh + hl) = 384
l^2 + b^2 + h^2 = 192
6. Find the Length:
- To find the length, we need to solve these equations simultaneously to get the value of l.
7. Conclusion:
- By solving the equations, we can find the length of the cuboid.
By following these steps and solving the equations accurately, you can determine the length of the cuboid using the given information about its total surface area and the sum of the squares of its dimensions.
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A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is?
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A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is? 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 A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is?.
A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is? 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 A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cuboid has a total surface area of 384 cm^2.The sum of the squares of its length, breadth and height is 192 cm^2.The length of the cuboid is?.
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