32 Centimeters

$Let\quad r\quad be\quad the\quad radius\quad of\quad the\quad circle\\ Let\quad t\quad be\quad the\quad time\\ \qquad \qquad r=4t\\ r=32,\\ \qquad \qquad 32=4t\\ \qquad \qquad t=8\\ Let\quad A\quad be\quad the\quad area\quad of\quad the\quad circle\\ A=\pi { r }^{ 2 }\\ Since\quad r=4t,\\ \qquad A=16\pi { t }^{ 2 }\\ \frac { dA }{ dt } =32\pi t\\ \\ Since\quad the\quad raidus\quad is\quad 32\quad when\quad the\quad time\quad is\quad 8,\\ \\ 32\pi (8)=256\pi \\ \\ \boxed { Therefore,\quad the\quad answer\quad is\quad 256\pi }$