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.


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