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For $z = a^{2} x^{3} y^{1 / 2},$ where $' a'$ is a constant. If percentage error in measurement of $' x'$ and $' y'$ are 4% and 12% respectively, then the percentage error for $' z'$ will be ...........%

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18%

20%

14%

12%

answer is A.

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Detailed Solution

$z = a^{2} x^{3} y^{1 / 2}$

$\frac{Δz}{z} \times 100 = 3 \frac{Δx}{x} \times 100 + \frac{1}{2} \frac{Δy}{y} \times 100$

$3 (4 %) + \frac{1}{2} (12 %) = 18 %$

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