Can somebody show me how to get to the answer? How do 2pi[((-6561/4)+2430-(729/2))-((-1/4)+(10/3)-(9/2))]=2560pi/3. My answer is always= 10184pi/12 or 2546pi/3. I don't know what I did wrong that cause my answer to be wrong.

2π[((-6561/4)+2430-(729/2))-((-1/4)+(10/3)-(9/2))]

= 2π[ 1701/4 - (-17/12) ]
= 2π [ 1280/3 ]
= 2560/3 π

I have a feeling you messed up in the subtraction of the terms in the second bracket.