DIY Scrubber - check my math

Did I do some math wrong? Or is my carbon weight per cubic inch wrong?

I'm DIY'ing a 16 inch scrubber. External radius = 3 inch, internal radius = 2 inches. (6 inch and 4 inch ducting)

If I do cylindrical volume, the 6 inch diameter cylinder's volume - the 4 inch one should give me the approximate cubic inches.

If I then multiply that by the weight in cubic inches, I should have my volume for my scrubber and I can source some bulk.

I'm getting ~450 cubic inches - 200 cubic inches ~= 250 cubic inches.

I found online that 1 cubic inch of carbon ~= 0.86 ounces.

So I need 215 ounces or 13 pounds of carbon?

No way a 16 inch scrubber is 13 pounds is it? (first time grower... never used one)

Is my .86 ounce weight wrong for a cubic inch of activated carbon? (source: http://www.aqua-calc.com/calculate/weight-to-volume/substance/activated-blank-carbon)

How many pounds of carbon do I need to fill my scrubber once?

So, 13 lbs is about right. If I was using smaller granulated carbon, it would be about 13 lbs.

I'm using pellets, and it takes about 9-10 lbs.