GATE 2021 MA – Question 48
Calculus · Multiple Integrals · 2 marks · Multiple choice
V is bounded by y=x²+z² and y=4. Evaluate $\iiint_V15\sqrt{x^2+z^2}\,dV$.
- 128π
- 64π
- 28π
- 256π
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Show answer and explanation
Correct answer: (A) 128π
Explanation
Use cylindrical coordinates about the y-axis: r²=x²+z²,0≤r≤2,r²≤y≤4,0≤θ≤2π, with Jacobian r. Integral=30π∫₀²r²(4−r²)dr=30π(32/3−32/5)=**128π, A**.
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