you are able to wrap a band tightly around a large sphere. The band would have a circumference about 40000 km. You insert into the band another strip 2m long so that the band will no longer fit tightly around the sphere. This new band would have a radius a little smaller than the previous band. About how far from the sphere would the new and larger band be.

Answer 1

Wouldn't the new band have a radius a little larger than the original?
I suspect a typo, and will assume it to be larger

C = 2πr
40000 = 2πr
r = 6366.197723676.. km

new circumference = 40000.002
new r = 6366.23676 km

difference = 0.00031831 km
= .31831 metres or appr 32 cm