###### Question 46 (Textile Engineering & Fibre Science)

If the error in the measurement of the diameter of a yarn is 0.5%, the error in the estimated cross-sectional area of this yarn would be

(A) | 0.25% |

(B) | 1.0% |

(C) | 2.5% |

(D) | 5.0% |

**[Show Answer]**

Given in the question-

Error in the measurement of the diameter of yarn=0.5%

Then, error in the estimated cross-sectional area of this yarn would be=?

By the formula-

Area of cylinder(yarn cross-section)=

Area of cylinder(yarn cross-section)

Cross-sectional area of yarn is directly proportional to the square of the diameter of the yarn

Now,

i.e , percentage error in cross-sectional area of yarn is twice the percentage error of the diameter of the yarn.

Where,

and

Percentage error in cross-sectional area of yarn=

Percentage error in cross-sectional area of yarn=1.0 (Ans)