$V=4t=\frac{4}{3}\pi {{r}^{3}}\xrightarrow{\pi =3}t={{r}^{3}}\Rightarrow r=\sqrt[3]{t}$  $S=4\pi {{r}^{2}}=4\times 3{{(\sqrt[3]{t})}^{2}}=12\sqrt[3]{{{t}^{2}}}\Rightarrow {S}'(1)=\underset{t\to 1}{\mathop{\lim }}\,\frac{12\sqrt[3]{{{t}^{2}}}-12}{t-1}$ $=12\underset{t\to 1}{\mathop{\lim }}\,\frac{(\sqrt[3]{{{t}^{2}}}-1)(\sqrt[3]{{{t}^{4}}}+\sqrt[3]{{{t}^{2}}}+1)}{(t-1)(\sqrt[3]{{{t}^{4}}}+\sqrt[3]{{{t}^{2}}}+1)}=12\underset{t\to 1}{\mathop{\lim }}\,\frac{t+1}{(\sqrt[3]{{{t}^{4}}}+\sqrt[3]{{{t}^{2}}}+1)}=12\times \frac{2}{3}=8$