Let R denote the solid torus (or solid donut), obtained byrevolving around the z-axis the circular disc (x ? b)2 + z2 ? a2 ,0 < a < b in the xz-plane. With ? denoting the angle ofrevolution around the z-axis (measured with counter- clockwiserotation), and with ? the angle given in the figure above, let G bygiven by 0???2?,0???2?,and0???a. The solid torus R is the image ofG by the mapping given by (x(?, ?, ?), y(?, ?, ?), z(?, ?, ?)) =((b + ? cos ?) cos ? , (b + ? cos ?) sin ? , ? sin ?) . Use thetriple integral and the change-of-variables formula to compute thevolume of R.
