ACJC Definite Integrals II Tutorial 23 Q2

The region \(R\) is bounded by the \(y\)-axis and the curves \(y=\sin x\) and \(y=\cos x\) for \(0\le x\le \frac{\pi }{4}\).

Find the volume of the solid of revolution formed when \(R\) is rotated through \(4\) right angles about the

1. \(x\)-axis
2. \(y\)-axis

giving your answers correct to \(3\) significant figures.