GATE 2022 MA – Question 59

Calculus · Vector Calculus · 2 marks · Numerical answer

Find the surface area of z=x²+y² between planes z=0 and z=1, to one decimal.

Show answer and explanation

Correct answer: 5.1 to 5.5

Explanation

The projection is r≤1 and the graph area element is √(1+4r²)r dr dθ. Area=2π∫₀¹r√(1+4r²)dr=(π/6)(5√5−1)≈**5.3**.

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