algebra problem?

Question

A company is decreasing the amount of tuna sold in a cylindrical can by 10%. The cans will have the same height but a smaller diameter. By what percent should the diameter decrease in order to accomodate the change?

Answer 1

For a cylinder, V = pi*r^2*h.
Let ro be the initial volume and rf the reduced volume. Then Vo= pi*ro^2*h and Vf=pi*rf^2*h.
Since Vf/Vo= 0.9 = rf^2/ro^2
rf is about 0.95*ro

Answer 2

pi*r1^2*h/pi*r^h=0.9
(r1/r)=sqrt(0.9)=0.94 thus decrease in diameter is 6%