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Finding the Radius of a Similar Sphere Given Volume

GEOM-99PXS3

A designer needs to design a spherical sculpture for the ballroom of a new hotel. He begins with a scale model that has a radius of $5.3\ cm$.

If the actual sphere should have a volume of $252,703.57\ cm^3$, what will be the radius of the actual sphere?

A

$0.72\ cm$

B

$39.22\ cm$

C

$106.69\ cm$

D

$2147.7\ cm$