Project ForgeEngineering Mathematics
Numerical Methods
GATE 2018
Hard
V=πh²(3R−h)/3 for liquid height h in a spherical tank of radius R. Estimate h (m) to store V=30m³ in R=3m tank after ONE iteration of the secant method, using 1m and 3m as initial guesses (rounded off to second decimal place)
1.9 m(± 0.05 accepted)
Explanation
f(h)=πh²(9−h)/3−30. f(1)=8.378−30=−21.62. f(3)=56.55−30=26.55. Secant: h_new=3−f(3)(3−1)/(f(3)−f(1))=3−26.55×2/48.17=3−1.10=1.90.
Source: GATE CH 2018 (2018)
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