The parametric equations are x = (cost)^3) and y = (sint)^3.

According to the symmetry, the volume v of the rotator is twice the volume of the graph enclosed by the curve and the coordinate axis rotating around the X axis in the first quadrant. Then you can get:

Extended data:

1, volume formula of rotating body

When rotating along the X axis, the radius =f(x), DV = π [f (x)] 2dx, and the integral V = ∫ π [f (x)] 2dx = π ∫ f (x) 2dx.

2. Wallace formula

There are only multiplication and division in Wallis formula, and even roots are not needed, so the form is very simple. Although Wallis formula has no direct influence on the approximate calculation of π, it plays an important role in the derivation of Stirling formula.

Huatouli's second formula:

∫(0→π/2)[(cos t)^n]dt=∫(0→π/2)[(sin t)^n]dt

=(n- 1)！ ! /n！ ! (n is a positive odd number)

=π(n- 1)！ ! /(2(n！ ! (n is a positive even number)