Let r be the radius of sphere, V be the volume and S be the surface area of the sphere.
Then,
V = 43πr3and S=4πr2
∴dVdt=43π(3r2)drdt=4πr2drdtAlso,dVdt=8 cm3/sec⇒8=4πr2drdt⇒drdt=2πr2 ...(i)
Now,
dSdt=4π(2r)drdt=8πrdrdt=8πr(2πr2) [using(i)]=16r cm2/secWhen r=12cm,dSdt=16r=1612=43=113cm2/s