A solid material has thermal conductivity K in kilowatts per meter$-$kelvin and temperature given at each point by

w$($x$,$y$,$z$)=15-4($x$^(2)+$y$^(2)+$z$^(2))\backslash$deg C$.$ Use the fact that heat flow is given by the vector field F$=-$Kgradw and the rate of heat

flow across a surface S within the solid is given by $-$K$\_($S$)$gradwdS$.$

Find the rate of heat flow out of a sphere of radius $1($centered at the origin$)$ inside a large cube of copper

$-$K$\_($S$)$gradwdS$=$

kW