In a cylindrical chamber fitted with a piston, the piston compresses \(10.0 \mathrm{~mol}\) of ideal gas from \(1.00 \mathrm{~m}^{3}\) to \(0.100 \mathrm{~m}^{3}\) at a constant temperature of \(300 \mathrm{~K}\). Suppose this compression was done by placing a \(100-\mathrm{kg}\) block on top of the piston. What is the piston radius? Assume the air pressure outside the piston is \(1.00 \mathrm{~atm}\), and ignore the piston mass.