Circle is easy but why are you rotating parabola

Geometry Level 4

A region is enclosed by the curves

  1. x 2 = 4 y x^{2 }= 4y
  2. x 2 = 4 y x^{2} =- 4y
  3. x = 4 x = 4
  4. x = 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 16 x^{2}+ y^{2} \leq 16

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

V (1)=1/2 V (2) π V ( 1 ) = V ( 2 ) \pi V (1)=V (2) V(1)=2V (2) No such relation exists. V (1)=V (2)

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