Problem
$\Rightarrow 2 \pi \int_{0}^{2} \frac{y^{3}}{3} \sqrt{1+y^{4}} d y$
Solution
Step 1 ：Calculate the definite integral: \(\Rightarrow 2 \pi \int_{0}^{2} \frac{y^{3}}{3} \sqrt{1+y^{4}} d y\)
Step 2 ：Final Answer: \(\boxed{24.1179}\)
