# Harry Potter And The Magical Sphere

**Geometry**Level 3

Harry Potter is playing with a Magic Sphere today, which remains as a sphere even as he changes it's physical properties.
He first increases the volume of Magic Sphere by \(20\%\).

Then he decreases the surface area by \(30\%\).

Compute \[\dfrac{\text{final radius of Magic Sphere}}{\text{original radius of Magic Sphere}} \; . \]

Give your answer to 3 decimal places.