Set up volumes, parametric lengths and surfaces of revolution
Coordinates are in metres. Give exact rational values; Vpi and Api mean the coefficients in \(V=\text{Vpi}\,\pi\,\text{m}^3\) and \(A=\text{Api}\,\pi\,\text{m}^2\). Circular-function arguments are in radians
Revolve the region between the curve and the y-axis, with the stated end bounds, about the y-axis. Give the disk radius at y=1 and Vpi
\[x=(3)y^{3},\qquad0\le y\le 1\]