GATE AG 2007 • Q1 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

An ellipsoidal object has three axes measuring 40 cm, 20 cm and 20 cm respectively. The volume of the object is

Options:

  • (A) 4.23 litres
  • (B) 8.38 litres
  • (C) 12.63 litres
  • (D) 17.05 litres

Official Answer Key:

B

Step-by-Step Solution & Explanation

Volume of an ellipsoid with semi-axes a, b, c: V = (4/3)π·a·b·c. Semi-axes = 20, 10, 10 cm. V = (4/3)π(20)(10)(10) = 8377.6 cm³ = 8.38 litres. (A) uses full axes as radii incorrectly halved twice; (C)/(D) come from using a sphere/cylinder formula instead of the ellipsoid formula.

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