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This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).
The lengths of sides of a cuboid are a, 2a and 3a. If the relative percentage error in the
measurement of a is 1%, then find the relative percentage error in the measurement of volume of cube (in percentage)….
    Correct answer is '3'. Can you explain this answer?
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    This section contains 5 questions. Each question, when worked out will...
    Solution:

    Given, the sides of the cuboid are a, 2a and 3a.

    Let the volume of the cuboid be V = a x 2a x 3a = 6a^3.

    The relative percentage error in the measurement of a is 1%.

    Therefore, the absolute error in the measurement of a is (1/100) x a = a/100.

    Calculating the relative percentage error in the measurement of volume:

    Using the formula for relative percentage error, we get:

    Relative percentage error in volume = (Absolute error in volume / Actual volume) x 100

    Absolute error in volume = (dV / da) x (a/100) [dV/dx denotes the derivative of V with respect to x]

    = (6a^2) x (a/100) = 3a^3/50

    Actual volume = 6a^3

    Therefore, relative percentage error in volume = [(3a^3/50) / (6a^3)] x 100

    = 1/2 x (3/50) x 100

    = 3%

    Hence, the relative percentage error in the measurement of volume of the cuboid is 3%.
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