GATE AG 2017 • Q26 NAT • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

The areas of seven horizontal cross-sections of a water reservoir at intervals of 9 m are 210, 250, 320, 350, 290, 230 and 170 m². The estimated volume of the reservoir in m³ using Simpson’s rule is __________.

Official Answer Key:

14760 to 14760

Step-by-Step Solution & Explanation

• Seven ordinates (n = 6 intervals, even number — Simpson’s 1/3 rule is directly applicable), spacing h = 9 m. • Simpson’s 1/3 rule: V = (h/3)[(A0+A6) + 4(A1+A3+A5) + 2(A2+A4)] • A0=210, A1=250, A2=320, A3=350, A4=290, A5=230, A6=170. • (A0+A6) = 210+170 = 380. • 4(A1+A3+A5) = 4(250+350+230) = 4(830) = 3320. • 2(A2+A4) = 2(320+290) = 2(610) = 1220. • V = (9/3)(380+3320+1220) = 3 × 4920 = 14760 m³.

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