Peruvian marinera

Calculus

Let there be a region $R:\{(x,y) \ | \ x^{1/4}+y^{4} \leq 1\}$ . What is the volume of the solid generated when $R$ is rotated around the line $x=0?$ Give your answer to 3 decimal places.

Note: You may use a calculator for the final step of your calculation.

Peruvian marinera

This question was posed by my calculus teacher as the last and higher value exercise on the third Calculus I test.