Cultured marble vanity-top & sink

How would I sand the integral sink in a 20-year-old cultured marble vanity top? Also, how would I remove grey (or black) lines in the bottom of the sink surrounding the pop-up drain?
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You can't. Cultured marble is made with a clear gelcoat over the colored materal. Any sanding or abrasive cleaner will take the gelcoat off - and any finish applied will quickly wear away.
Vanity tops are not expensive or hard to replace. Stop by your local big box store and take a look at new ones.
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Its probably mold, let laundry bleach soak it for maybe 10 minutes, it might help and wont hurt.
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