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GATE 2019 ME (ME1) – Question 12

Engineering Mathematics · Calculus: Definite and improper integrals, double and triple integrals · 1 mark · Multiple choice

The parabola $x=y^2$, $0\le x\le1$, bounds the shaded region shown. Find the volume generated by rotating this region through 360° about the x-axis.

Diagram for GATE 2019 ME (ME1) question 12
  1. $\pi/4$
  2. $\pi/2$
  3. $\pi$
  4. $2\pi$

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Show answer and explanation

Correct answer: (B) $\pi/2$

Explanation

Use circular disks perpendicular to the x-axis. Their area is $\pi y^2=\pi x$, hence $V=\pi\int_0^1x\,dx=\pi/2$. **Answer: B**. The radius is y, so it must be squared before integrating.