Peruvian marinera

Calculus Level 4

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.

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

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