S1＝4πR1²
S2＝4πR2²
S1∶S2＝4πR1²∶4πR2²=R1²∶R2²＝1∶2
∴R2＝√2R1
V1＝4π/3R1³
V2＝4π/3R2³
V1∶V2＝4π/3R1³∶4π/3R2³
＝R1³∶R2³
＝R1³∶（√2R1）³
＝1∶（√2）³
＝1∶2√2
∴V2∶V1＝2√2
答：体积扩大为原来的2√2倍.