While riding a multispeed bicycle, the rider can select the radius of the rear sprocket that is fixed to the rear axle. The front sprocket of a bicycle has radius $14\mathrm{.}0cm.$

Part A

If the angular speed of the front sprocket is $0\mathrm{.}700re\frac{v}{s},$ what is the radius of the rear sprocket for which the tangential speed of a point on the rim of the rear wheel will be $4\mathrm{.}50\frac{m}{s}?$ The rear wheel has radius $0\mathrm{.}350m.$

Express your answer in meters.