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Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3
A = 50.0 cm +/-.04 cm
B = 40.0 cm +/-.03 cm
C = 30.0 cm + /-.02 cm
Correct answer is '77'. Can you explain this answer?
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The standard error of the volume of a cuboid can be calculated by considering the standard errors of each side length. In this case, the standard errors of the side lengths A, B, and C are given as follows:
A = 50.0 cm ± 0.04 cm
B = 40.0 cm ± 0.03 cm
C = 30.0 cm ± 0.02 cm
To calculate the standard error of the volume, we need to consider the partial derivatives of the volume with respect to each side length. The volume of a cuboid is given by the formula:
V = A * B * C
Let's calculate the standard error step by step:
1. Calculate the partial derivative of the volume with respect to A:
∂V/∂A = B * C
2. Calculate the partial derivative of the volume with respect to B:
∂V/∂B = A * C
3. Calculate the partial derivative of the volume with respect to C:
∂V/∂C = A * B
4. Calculate the standard error of the volume using the formula:
SE(V) = sqrt((SE(A) * ∂V/∂A)^2 + (SE(B) * ∂V/∂B)^2 + (SE(C) * ∂V/∂C)^2)
Substituting the given values:
SE(V) = sqrt((0.04 * B * C)^2 + (0.03 * A * C)^2 + (0.02 * A * B)^2)
5. Substituting the values of A, B, and C:
SE(V) = sqrt((0.04 * 40.0 * 30.0)^2 + (0.03 * 50.0 * 30.0)^2 + (0.02 * 50.0 * 40.0)^2)
6. Simplifying the expression:
SE(V) = sqrt(57600 + 13500 + 16000)
7. Calculating the square root:
SE(V) = sqrt(87100)
8. Rounding the result to the nearest whole number:
SE(V) ≈ 77
Therefore, the standard error of the volume of the cuboid is approximately 77 cm³.
A = 50.0 cm ± 0.04 cm
B = 40.0 cm ± 0.03 cm
C = 30.0 cm ± 0.02 cm
To calculate the standard error of the volume, we need to consider the partial derivatives of the volume with respect to each side length. The volume of a cuboid is given by the formula:
V = A * B * C
Let's calculate the standard error step by step:
1. Calculate the partial derivative of the volume with respect to A:
∂V/∂A = B * C
2. Calculate the partial derivative of the volume with respect to B:
∂V/∂B = A * C
3. Calculate the partial derivative of the volume with respect to C:
∂V/∂C = A * B
4. Calculate the standard error of the volume using the formula:
SE(V) = sqrt((SE(A) * ∂V/∂A)^2 + (SE(B) * ∂V/∂B)^2 + (SE(C) * ∂V/∂C)^2)
Substituting the given values:
SE(V) = sqrt((0.04 * B * C)^2 + (0.03 * A * C)^2 + (0.02 * A * B)^2)
5. Substituting the values of A, B, and C:
SE(V) = sqrt((0.04 * 40.0 * 30.0)^2 + (0.03 * 50.0 * 30.0)^2 + (0.02 * 50.0 * 40.0)^2)
6. Simplifying the expression:
SE(V) = sqrt(57600 + 13500 + 16000)
7. Calculating the square root:
SE(V) = sqrt(87100)
8. Rounding the result to the nearest whole number:
SE(V) ≈ 77
Therefore, the standard error of the volume of the cuboid is approximately 77 cm³.
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Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer?
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Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer?.
Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the standard error of the volume of a cuboid whose sides are A, B, and C have values given below and standard error as +/-___________ in cm3A = 50.0 cm +/-.04 cmB = 40.0 cm +/-.03 cmC = 30.0 cm + /-.02 cmCorrect answer is '77'. Can you explain this answer?.
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