Let the radius of the half roll of paper be r.
The area of the original roll of paper is pi*(6^2 – 2^2) = 32pi
So half of this area would be 32/2pi = 16pi.
Including the tube, it would be 16pi+4pi=20pi.
So, the area of half roll of paper is pi*(r^2) = 20pi
Therefore r = sqrt(20) which is about 4.5.
But we are looking for the diameter, which is 4.5*2= 9cm #
Very tricky question! I hope it is the right answer.