# Circle is easy but why are you rotating parabola

**Geometry**Level 4

A region is enclosed by the curves

- \[x^{2 }= 4y \]
- \[x^{2} =- 4y\]
- \[x = 4 \]
\[x =- 4\] 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

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

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

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