GATE (TF) Textile 2012 Question Paper Solution | GATE/2012/TF/35

Question 35 (Textile Engineering & Fibre Science)

A yarn of 24 mm length has a varying cross-section. The values of the cross-sectional area of yarn (mm2), measured at equal intervals of 4 mm from one end are
0.09, 0.12, 0.14, 0.15, 0.16, 0.13, 0.11
The volume of yarn (mm3) estimated by using Simpsons 1/3 rule of numerical integration is

(A)2.40
(B)2.80
(C)3.20
(D)3.36
Answer / Solution
Table-
y(0)y(1)y(2)y(3)y(4)y(5)
x(mm2)048121624
y(mm3)0.090.120.140.150.160.11

Total length =24mm
Simpsons 1/3 rule-
Volume of yarn=\pi \times r^2 \times h
=\frac{h}{3}[(y0+y5)+2(y2+y4)+4(y1+y3+y5)]
=\frac{4}{3}[(0.09+0.11)+2(0.14+0.16)+4(0.12+0.15+0.13)]
=3.2 (Ans)
Option C is correct.

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