V = 4/3πR3(t) = ct
两边求导:
4πR2(t)R’(t) = c
R(t)R’(t) = c/(4πR(t))
球表面积:
A(t) = 4πR2(t)
两边求导:
A’(t) = 8πR(t)R’(t) = 8π*c/(4πR(t))
= 2c/(R(t))
球的表面积的增长速度与球半径成反比,比例系数为2c.