Circle is easy but why are you rotating parabola

Geometry Level 4

A region is enclosed by the curves

  1. \[x^{2 }= 4y \]
  2. \[x^{2} =- 4y\]
  3. \[x = 4 \]
  4. \[x =- 4\] V(1) is the volume of the solid obtained by rotating the above region round the y-axis.

    Another region consists of points (x, y) satisfying

  5. \[x^{2}+ y^{2} \leq 16\]

  6. \[x^{2}+ (y - 2)^{2} \geq 4\]
  7. \[x^{2} + ( y + 2)^{2} \geq 4\]

V(2) is the volume of the solid obtained by rotating this region round the y-axis. Then

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