# 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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